# Programs for A350000-A399999

List of integer sequences with links to LODA programs.

- A350008 (program): a(n) = Sum_{k=0..n} k^(2*k).
- A350037 (program): a(n) = n^2 mod round(sqrt(n)).
- A350042 (program): Sum of all the parts in the partitions of n into 3 positive integer parts.
- A350050 (program): a(n) = (2*n^4 - 6*(-1)^n*n^2 - 2*n^2 + 3*(-1)^n - 3)/96.
- A350051 (program): Part three of the trisection of A017101: a(n) = 19 + 24*n.
- A350052 (program): Third part of the trisection of A017077: a(n) = 17 + 24*n.
- A350053 (program): a(n) = (2^(3*n + 3 + (-1)^n) - (6 + (-1)^n))/9, for n >= 1.
- A350054 (program): a(n) = (4^(3*n+2) - 7)/9, n >= 1.
- A350055 (program): a(n) = 36*n + 35, for n >= 0.
- A350072 (program): a(n) = sigma(n^2) / gcd(sigma(n^2), A003961(n^2)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of divisors function.
- A350073 (program): a(n) = A064989(sigma(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p.
- A350090 (program): a(n) is the number of indices i in the range 0 <= i <= n-1 such that A003215(n) - A003215(i) is an oblong number (A002378), where A003215 are the hex numbers.
- A350091 (program): a(n) = a(floor(n/4)) for n == 2 (mod 4), otherwise n.
- A350094 (program): a(n) = Sum_{k=0..n} n CNIMPL k where CNIMPL = NOT(n) AND k is the bitwise logical converse non-implication operator (A102037).
- A350102 (program): Number of self-measuring subsets of the initial segment of the natural numbers strictly below n. Number of subsets S of [n] with S = distset(S).
- A350104 (program): a(n) = Sum_{k=0..n} A350102(k).
- A350105 (program): Number of subsets of the initial segment of the natural numbers strictly below n which are not self-measuring. Number of subsets S of [n] with S != distset(S).
- A350107 (program): a(n) = Sum_{k=1..n} k * floor(n/k)^2.
- A350108 (program): a(n) = Sum_{k=1..n} k * floor(n/k)^3.
- A350109 (program): a(n) = Sum_{k=1..n} k * floor(n/k)^n.
- A350116 (program): Number of ways to partition the set of vertices of a convex {n+8}-gon into 3 non-intersecting polygons.
- A350123 (program): a(n) = Sum_{k=1..n} k^2 * floor(n/k)^2.
- A350124 (program): a(n) = Sum_{k=1..n} k^2 * floor(n/k)^3.
- A350125 (program): a(n) = Sum_{k=1..n} k^2 * floor(n/k)^n.
- A350128 (program): a(n) = Sum_{k=1..n} k^n * floor(n/k)^2.
- A350134 (program): Number of endofunctions on [n] with at least one isolated fixed point.
- A350143 (program): a(n) = Sum_{k=1..n} floor(n/(2*k-1))^2.
- A350144 (program): a(n) = Sum_{k=1..n} floor(n/(2*k-1))^3.
- A350145 (program): a(n) = Sum_{k=1..n} floor(n/(2*k-1))^n.
- A350146 (program): Partial sums of A002131.
- A350156 (program): Inverse Moebius transform of A000056.
- A350159 (program): Number of subgroups of the dicyclic group Dic_n.
- A350162 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^2.
- A350163 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/(2*k-1))^3.
- A350164 (program): a(n) = Sum_{k=1..n}(-1)^(k+1) * floor(n/(2*k-1))^n.
- A350166 (program): Partial sums of A050469.
- A350168 (program): Count from 0 to 1st prime 2, then from 0 to 2nd prime 3, then from 0 to 3rd prime 5, etc …
- A350169 (program): Write 1st prime and decrement 0 times, then write 2nd prime and decrement once, write 3rd prime and decrement twice, write 4th prime and decrement 3 times, etc …
- A350171 (program): Add 1 to the 1st prime, then write the 2nd prime, then add 1 to the 3rd prime, then write the 4th prime, etc., alternately adding a 1 or not.
- A350172 (program): Start from 1st prime 2, and write it twice, then add 3 to get 5 and write it 3 times, then add 5 to get 10 and write it 5 times, and so on.
- A350173 (program): Write the square of 1st prime, then the 2nd prime, then the square of 3rd prime, alternately squaring or not.
- A350178 (program): Take n and subtract the greatest square less than or equal to n. Repeat this process until 0 is reached. a(n) is the sum of all residues after subtractions.
- A350229 (program): a(n) is the sum of n and the balanced ternary digits in n.
- A350267 (program): a(n) = n*hypergeom([1, 1 - n, -n], [2], 1) if n >= 1, a(0) = 1.
- A350268 (program): a(n) = Sum_{k=0..n} (n - k)! * (n - 1)^k. Row sums of A350269.
- A350286 (program): Number of different ways to partition the set of vertices of a convex (n+11)-gon into 4 nonintersecting polygons.
- A350290 (program): a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n, k) * binomial(n + k - 1, n - k).
- A350294 (program): a(n) = floor(n*2^n/(n + 1)).
- A350295 (program): 2nd subdiagonal of the triangle A350292.
- A350303 (program): a(n) is the number of ways to partition the set of vertices of a convex (n+14)-gon into 5 nonintersecting polygons.
- A350309 (program): a(n) = (n+2)*a(n-1) + (n+1)*(A003422(n) - 4)/6 for n > 0 with a(0) = 1.
- A350314 (program): The catch-up points of the Redstone permutation A350313.
- A350315 (program): Length of the rows of the Redstone permutation A350313.
- A350327 (program): Maximum domination number of connected graphs with n vertices and minimum degree 2.
- A350361 (program): 2-tone chromatic number of a tree with maximum degree n.
- A350362 (program): 2-tone chromatic number of an n-cycle.
- A350382 (program): a(n) = 9 + 4 * 10^n.
- A350383 (program): a(n) = [x^n] 1/(1 + x + x^2)^n.
- A350384 (program): a(n) = (-1728)^n.
- A350387 (program): a(n) is the sum of the odd exponents in the prime factorization of n.
- A350388 (program): a(n) is the largest unitary divisor of n that is a square.
- A350389 (program): a(n) is the largest unitary divisor of n that is an exponentially odd number (A268335).
- A350390 (program): a(n) is the largest exponentially odd divisor of n.
- A350395 (program): Numbers m such that a term with the largest coefficient in Product_{k=1..m} (1 + x^k) is unique.
- A350396 (program): Numbers m such that there are two or more terms with the largest coefficient in Product_{k=1..m} (1 + x^k).
- A350461 (program): Number of ways to choose a subset of size n from [2n] and arrange its elements into a set of lists.
- A350467 (program): a(n) = hypergeom([1/2 - n/2, -n/2], [-n], -8*n).
- A350468 (program): a(n) = hypergeom([1/2 - n/2, -n/2], [-n], -56).
- A350469 (program): a(n) = hypergeom([1/2 - n/2, -n/2], [-n], -72).
- A350471 (program): The number of days elapsed since the Gregorian date Sunday, December 31, 1 BC on 1/1/n, where 1/1/n is the Gregorian date in the format month/day/year, the New Year’s Day of the year n.
- A350473 (program): a(n) = Fibonacci(n+1)^3 - Fibonacci(n-1)^3.
- A350493 (program): a(n) = floor(sqrt(prime(n)))^2 mod n.
- A350498 (program): Convolution of triangular numbers with every third number of Narayana’s Cows sequence.
- A350509 (program): a(n) = n/A055874(n).
- A350512 (program): Triangle read by rows with T(n,0) = 1 for n >= 0 and T(n,k) = binomial(n-1,k-1)*(2*k*(n-k) + n)/k for 0 < k <= n.
- A350520 (program): The number of degree-n^2 polynomials over Z/2Z that can be written as f(f(x)) where f is a polynomial.
- A350521 (program): a(n) = 18*n + 4.
- A350522 (program): a(n) = 18*n + 16.
- A350526 (program): a(n) = f(n*r)*c(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622).
- A350527 (program): a(n) = c(n*r)*f(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622).
- A350551 (program): Convolution of Jacobsthal numbers and Pell numbers.
- A350567 (program): a(n) is the maximum number of key comparisons required to perform an indirect sort of n records with distinct keys using a two-way merge (A. D. Woodall’s mergesort).
- A350576 (program): a(n) = n/A055874(n) - A055874(n).
- A350634 (program): Products of the parts s,t in each partition of k (= 2,3,..) into two parts, ordered by increasing k and then by increasing values of s*t (see example).
- A350637 (program): Triangle read by rows: T(n,k) in which row n lists the first n terms of A024916 in reverse order, 1 <= k <= n.
- A350652 (program): a(n) is where the chosen card needs to be placed in a deck of 2n cards when performing “Persistimis Possessiamo” trick.
- A350653 (program): a(n) is the number of weak compositions of n into n-1 parts in which at least one part is zero.
- A350661 (program): a(1) = 1; a(n) = a(A007947(n) - 1) + n.
- A350666 (program): Numbers congruent to 0, 5, and 7 modulo 9: positions of 0 in A159955.
- A350667 (program): Numbers congruent to 1, 3, and 8 modulo 9: positions of 1 in A159955.
- A350668 (program): Numbers congruent to 2, 4, and 6 modulo 9: positions of 2 in A159955.
- A350669 (program): Numerators of Sum_{j=0..n} 1/(2*j+1), for n >= 0.
- A350670 (program): Denominators of Sum_{j=0..n} 1/(2*j+1), for n >= 0.
- A350678 (program): Partial sums of A185381.
- A350689 (program): a(n) = n*(1 - (-1)^n - 2*(3 + (-1)^n)*n^2 + 2*n^4)/384.
- A350698 (program): Consider the positive squares summing to n as obtained by the greedy algorithm; a(n) is the least of these squares.
- A350716 (program): a(n) is the minimum number of vertices of degree 3 over all 3-collapsible graphs with n vertices.
- A350749 (program): Triangle read by rows: T(n,k) is the number of oriented graphs on n labeled nodes with k arcs, n >= 0, k = 0..n*(n-1)/2.
- A350757 (program): a(1)=1; for n>1, a(n) is the smallest number k > a(n-1) such that a(n-1) + k is not a square.
- A350770 (program): Triangle read by rows: T(n, k) = 2^(n-k-1) + 2^k - 2, 0 <= k <= n-1.
- A350771 (program): Triangle read by rows: T(n, k) = (2^(n-k-1) + 2^k - 2)*binomial(n-1, k), 0 <= k <= n-1.
- A350801 (program): a(n) = n*(tau(n) + 1) - 2*sigma(n) for n>=1, with a(0)=0.
- A350851 (program): Cumulative sums of the first ceiling(n/2)+1 elements of rows 0 to n in Pascal’s triangle.
- A350855 (program): a(0) = 1, a(n) = (n+1)*a(n-1) + (n-2).
- A350869 (program): a(n) = Sum_{i=0..10^n-1} i^3.
- A350872 (program): Number of coincidence site lattices of index n in square lattice.
- A350895 (program): a(n) = 1 + a(n-1) * prime(n), starting a(0) = 1.
- A350917 (program): a(0) = 1, a(1) = 2, and a(n) = 23*a(n-1) - a(n-2) - 4 for n >= 2.
- A350919 (program): a(0) = 9, a(1) = 9, and a(n) = 3*a(n-1) - a(n-2) - 4 for n >= 2.
- A350920 (program): a(0) = 5, a(1) = 5, and a(n) = 4*a(n-1) - a(n-2) - 4 for n >= 2.
- A350921 (program): a(0) = 3, a(1) = 3, and a(n) = 6*a(n-1) - a(n-2) - 4 for n >= 2.
- A350922 (program): a(0) = 2, a(1) = 5, and a(n) = 7*a(n-1) - a(n-2) - 4 for n >= 2.
- A350923 (program): a(0) = 2, a(1) = 2, and a(n) = 10*a(n-1) - a(n-2) - 4 for n >= 2.
- A350924 (program): a(0) = 1, a(1) = 3, and a(n) = 16*a(n-1) - a(n-2) - 4 for n >= 2.
- A350925 (program): a(0) = 1, a(1) = 9, and a(n) = 16*a(n-1) - a(n-2) - 4 for n >= 2.
- A350926 (program): a(0) = 1, a(1) = 17, and a(n) = 23*a(n-1) - a(n-2) - 4 for n >= 2.
- A350961 (program): a(n) = Sum_{k=1..n} 3^Omega(k).
- A350962 (program): a(n) = A068527(2*n).
- A350965 (program): a(n) = sqrt(6*A138288(n)^2 - 2).
- A350966 (program): a(n) = sqrt(28*A296377(n)^2 - 3).
- A350967 (program): a(n) = sqrt(84*A144930(n)^2 - 3).
- A350968 (program): a(n) = (A350967(n)-1)/2.
- A350973 (program): T(n,n-5), where T(*,*) is A350970.
- A350979 (program): a(0)=1, a(1)=652, thereafter a(n) = 254*a(n-1)-a(n-2)+378.
- A350980 (program): a(0)=17, a(1)=4700, thereafter a(n) = 254*a(n-1)-a(n-2)+378.
- A350981 (program): Union of A350979 and A350980.
- A350982 (program): a(0)=0, a(1)=49, thereafter a(n) = 14*a(n-1)-a(n-2)+42.
- A350983 (program): a(0)=1, a(1)=25, a(2)=865; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
- A350984 (program): a(0)=0, a(1)=18, a(2)=612; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
- A350985 (program): a(0)=4, a(1)=148, a(2)=5044; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
- A350986 (program): a(0)=3, a(1)=105, a(2)=3567; a(n) = 35*(a(n-1)-a(n-2))+a(n-3).
- A350994 (program): a(n) = (40*100^n + 6*10^n - 1)/3.
- A350995 (program): a(n) = (16*10^n-1)/3.
- A350996 (program): a(n) = Sum_{k=1..n} k * rad(k).
- A350997 (program): a(n) = Sum_{k=1..n} k^rad(k).
- A351046 (program): a(1)=1; a(2)=4; for n>2, a(n) = a(n-1) + A000217(n)*a(n-2).
- A351058 (program): Number of numbers <= n that are either nonprime divisors of n or primes not dividing n.
- A351083 (program): a(n) = gcd(n, A003415(A276086(n))), where A003415 is the arithmetic derivative and A276086 converts the primorial base expansion of n into its prime product form.
- A351090 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A351091(i) = A351091(j) and A351092(i) = A351092(j), for all i, j >= 1.
- A351114 (program): Characteristic function of balanced numbers.
- A351115 (program): Number of balanced numbers <= n.
- A351153 (program): Triangle read by rows: T(n, k) = n*(k - 1) - k*(k - 3)/2 with 0 < k <= n.
- A351193 (program): Sum of the 5th powers of primes dividing n.
- A351194 (program): Sum of the 6th powers of the primes dividing n.
- A351195 (program): Sum of the 7th powers of the primes dividing n.
- A351196 (program): Sum of the 8th powers of the primes dividing n.
- A351197 (program): Sum of the 9th powers of the primes dividing n.
- A351198 (program): Sum of the 10th powers of the primes dividing n.
- A351225 (program): a(n) = A276086(n) - n, where A276086 is the primorial base exp-function.
- A351231 (program): Denominator of A003415(n) / A276086(n), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
- A351232 (program): a(n) = floor(A276086(n) / A003415(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.
- A351238 (program): Numbers M such that 87 * M = 1M1, where 1M1 denotes the concatenation of 1, M and 1.
- A351242 (program): a(n) = n^3 * Sum_{p|n, p prime} 1/p^3.
- A351244 (program): a(n) = n^4 * Sum_{p|n, p prime} 1/p^4.
- A351245 (program): a(n) = n^5 * Sum_{p|n, p prime} 1/p^5.
- A351246 (program): a(n) = n^6 * Sum_{p|n, p prime} 1/p^6.
- A351247 (program): a(n) = n^7 * Sum_{p|n, p prime} 1/p^7.
- A351248 (program): a(n) = n^8 * Sum_{p|n, p prime} 1/p^8.
- A351249 (program): a(n) = n^9 * Sum_{p|n, p prime} 1/p^9.
- A351250 (program): Numerator of n / A276086(n).
- A351251 (program): Denominator of n / A276086(n).
- A351262 (program): a(n) = n^10 * Sum_{p|n, p prime} 1/p^10.
- A351265 (program): Sum of the squares of the squarefree divisors of n.
- A351266 (program): Sum of the cubes of the squarefree divisors of n.
- A351267 (program): Sum of the 4th powers of the squarefree divisors of n.
- A351268 (program): Sum of the 5th powers of the squarefree divisors of n.
- A351269 (program): Sum of the 6th powers of the squarefree divisors of n.
- A351270 (program): Sum of the 7th powers of the squarefree divisors of n.
- A351271 (program): Sum of the 8th powers of the squarefree divisors of n.
- A351272 (program): Sum of the 9th powers of the squarefree divisors of n.
- A351273 (program): Sum of the 10th powers of the squarefree divisors of n.
- A351279 (program): a(n) = Sum_{k=0..n} 2^k * k^(n-k).
- A351282 (program): a(n) = Sum_{k=0..n} 3^k * k^(n-k).
- A351283 (program): G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^4.
- A351300 (program): a(n) = n^5 * Product_{p|n, p prime} (1 + 1/p^5).
- A351301 (program): a(n) = n^6 * Product_{p|n, p prime} (1 + 1/p^6).
- A351302 (program): a(n) = n^7 * Product_{p|n, p prime} (1 + 1/p^7).
- A351303 (program): a(n) = n^8 * Product_{p|n, p prime} (1 + 1/p^8).
- A351304 (program): a(n) = n^9 * Product_{p|n, p prime} (1 + 1/p^9).
- A351305 (program): a(n) = n^10 * Product_{p|n, p prime} (1 + 1/p^10).
- A351307 (program): Sum of the squares of the square divisors of n.
- A351308 (program): Sum of the cubes of the square divisors of n.
- A351309 (program): Sum of the 4th powers of the square divisors of n.
- A351310 (program): Sum of the 5th powers of the square divisors of n.
- A351311 (program): Sum of the 6th powers of the square divisors of n.
- A351313 (program): Sum of the 7th powers of the square divisors of n.
- A351314 (program): Sum of the 8th powers of the square divisors of n.
- A351315 (program): Sum of the 9th powers of the square divisors of n.
- A351316 (program): Sum of the 10th powers of the square divisors of n.
- A351331 (program): a(n) = (n+1)*n^n + n - 1.
- A351340 (program): a(n) = Sum_{k=0..n} n^k * k^(n-k).
- A351347 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(-s) - 2*p^(-2*s)).
- A351355 (program): Number of ways the numbers from 1..n do not divide numbers from n+1..2n.
- A351362 (program): Number of ways the numbers from 1..n do not divide the numbers from n..2n-1.
- A351366 (program): a(n) = Sum_{p|n, p prime} p^p.
- A351371 (program): a(n) = Sum_{p|n, p prime} (p + n/p).
- A351394 (program): Number of divisors of n that are either squarefree, prime powers, or both.
- A351397 (program): Sum of the exponents in the prime factorizations of the prime power divisors of n.
- A351412 (program): a(1) = 1, a(2) = 2, a(3) = 3. Then if n is even a(n) is the least positive integer not yet in the sequence, otherwise if n is odd a(n) = a(n-1) + a(n-3).
- A351434 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)^(k_j + 1)).
- A351435 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)^(k_j + 1)).
- A351450 (program): a(n) = A064989(A048250(A003961(n))).
- A351454 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A329697(i) = A329697(j) and A331410(i) = A331410(j) for all i, j >= 1.
- A351460 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A206787(i) = A206787(j) and A336651(i) = A336651(j) for all i, j >= 1.
- A351519 (program): a(n) = tau(n) + pi(n) - omega(n).
- A351521 (program): Dirichlet g.f.: Product_{p prime} (1 + 4*p^(-s)).
- A351529 (program): The number of quaternary strings of length n containing 00.
- A351530 (program): The number of quinary strings of length n containing 00.
- A351531 (program): a(0)=1; a(1)=1; for n>1, a(n) = a(n-1) + 3*n*a(n-2).
- A351544 (program): a(n) is the largest unitary divisor of sigma(n) such that its every prime factor also divides A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
- A351546 (program): a(n) is the largest unitary divisor of sigma(n) coprime with A003961(n), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
- A351561 (program): a(n) = n + d(n) - phi(n), where d is the number of divisors function, and phi is the Euler totient function.
- A351580 (program): a(n) is the number of multisets of size n-1 consisting of permutations of n elements.
- A351600 (program): a(n) = n^2 * Sum_{d^2|n} 1 / d^2.
- A351601 (program): a(n) = n^3 * Sum_{d^2|n} 1 / d^3.
- A351602 (program): a(n) = n^4 * Sum_{d^2|n} 1 / d^4.
- A351603 (program): a(n) = n^5 * Sum_{d^2|n} 1 / d^5.
- A351604 (program): a(n) = n^6 * Sum_{d^2|n} 1 / d^6.
- A351605 (program): a(n) = n^7 * Sum_{d^2|n} 1 / d^7.
- A351606 (program): a(n) = n^8 * Sum_{d^2|n} 1 / d^8.
- A351607 (program): a(n) = n^9 * Sum_{d^2|n} 1 / d^9.
- A351608 (program): a(n) = n^10 * Sum_{d^2|n} 1 / d^10.
- A351619 (program): a(n) = Sum_{p|n, p prime} (-1)^p.
- A351635 (program): a(n) is the number of perfect matchings of an edge-labeled 2 X n Klein bottle grid graph, or equivalently the number of domino tilings of a 2 X n Klein bottle grid. (The twist is on the length-n side.)
- A351647 (program): Sum of the squares of the odd proper divisors of n.
- A351654 (program): Dirichlet g.f.: zeta(s) / (zeta(s-1) * zeta(s-2)).
- A351697 (program): 32*a(n) is the denominator of the squared circumradius of a cyclic quadrilateral with sides n, n+1, n+2, n+3.
- A351702 (program): In the balanced ternary representation of n, reverse the order of digits other than the most significant.
- A351706 (program): For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the denominator of d(n) = Sum_{k >= 0} b_k * 2^A130472(k). See A351705 for the numerators.
- A351749 (program): a(n) = Sum_{p|n, p prime} sigma_p(p).
- A351760 (program): a(n) = Sum_{1 <= i < j <= n} (i*j)^4.
- A351762 (program): Expansion of e.g.f. 1/(1 - 2*x*exp(x)).
- A351763 (program): Expansion of e.g.f. 1/(1 - 3*x*exp(x)).
- A351765 (program): a(n) = n! * Sum_{k=0..n} n^(n-k) * (n-k)^k/k!.
- A351766 (program): a(n) = Sum_{j=1..n} Sum_{i=1..j} (i*j)^4.
- A351768 (program): a(n) = n! * Sum_{k=0..n} k^(n-k) * (n-k)^k/k!.
- A351770 (program): a(n) = Sum_{j=1..n} Sum_{i=1..j} (i*j)^5.
- A351777 (program): Expansion of e.g.f. 1/(1 + 2*x*exp(x)).
- A351778 (program): Expansion of e.g.f. 1/(1 + 3*x*exp(x)).
- A351779 (program): a(n) = n! * Sum_{k=0..n} (-n)^(n-k) * (n-k)^k/k!.
- A351780 (program): a(n) = n! * Sum_{k=0..n} (-k)^(n-k) * (n-k)^k/k!.
- A351782 (program): a(n) = n-2 if n is a multiple of 4, a(n) = n-1 otherwise.
- A351792 (program): Expansion of e.g.f. 1/(1 - x*exp(-3*x)).
- A351793 (program): Expansion of e.g.f. 1/(1 - x*exp(-4*x)).
- A351795 (program): a(n) = n! * Sum_{k=0..n} (k * (n-k))^k/k!.
- A351796 (program): a(n) = n! * Sum_{k=0..n} (-k * (n-k))^k/k!.
- A351805 (program): a(n) = Sum_{1 <= i < j <= n} j^5*i^5.
- A351825 (program): Total number of size 2 lists in all sets of lists partitioning [n] (cf. A000262).
- A351827 (program): Sum of the numbers <= n that are either prime, a divisor of n, or both.
- A351843 (program): a(n) = sigma(n) * sopf(n).
- A351846 (program): Irregular triangle read by rows: T(n,k), n >= 0, k >= 0, in which n appears 4*n + 1 times in row n.
- A351905 (program): Expansion of e.g.f. exp(x * (1 - x^3)).
- A351911 (program): a(n) is the least integer m such that every m-element subset of {1,2,3,…,n} contains two nonempty and disjoint subsets whose sums are equal.
- A351914 (program): Numbers m such that the average of the prime numbers up to m is greater than or equal to m/2.
- A351923 (program): Number of ordered pairs of positive integers (s,t), s,t <= n, such that (s^t) | n.
- A351929 (program): Expansion of e.g.f. exp(x - x^3/6).
- A351930 (program): Expansion of e.g.f. exp(x - x^4/24).
- A351932 (program): Number of set partitions of [n] such that block sizes are either 1 or 4.
- A351974 (program): a(n) is the first maximum reached by iterating the reduced Collatz function R on 4n-1: a(n) = R^s(4n-1), where R(k) = A139391(k) and s the number of iterations required.
- A351985 (program): If n = abcd… in decimal, a(n) = |a^3 - b^3 + c^3 - d^3 + …|.
- A351992 (program): Number of minimum edge covers in the n-vertex wheel graph.
- A352002 (program): a(n) = prime(n)# + prime(n), where prime(n)# is the n-th primorial number A002110(n).
- A352030 (program): Numbers n for which every part of the symmetric representation of sigma(n) has maximum width 2.
- A352031 (program): Sum of the cubes of the odd proper divisors of n.
- A352032 (program): Sum of the 4th powers of the odd proper divisors of n.
- A352033 (program): Sum of the 5th powers of the odd proper divisors of n.
- A352034 (program): Sum of the 6th powers of the odd proper divisors of n.
- A352035 (program): Sum of the 7th powers of the odd proper divisors of n.
- A352036 (program): Sum of the 8th powers of the odd proper divisors of n.
- A352037 (program): Sum of the 9th powers of the odd proper divisors of n.
- A352038 (program): Sum of the 10th powers of the odd proper divisors of n.
- A352047 (program): Sum of the divisor complements of the odd proper divisors of n.
- A352048 (program): Sum of the squares of the divisor complements of the odd proper divisors of n.
- A352049 (program): Sum of the cubes of the divisor complements of the odd proper divisors of n.
- A352050 (program): Sum of the 4th powers of the divisor complements of the odd proper divisors of n.
- A352051 (program): Sum of the 5th powers of the divisor complements of the odd proper divisors of n.
- A352052 (program): Sum of the 6th powers of the divisor complements of the odd proper divisors of n.
- A352053 (program): Sum of the 7th powers of the divisor complements of the odd proper divisors of n.
- A352054 (program): Sum of the 8th powers of the divisor complements of the odd proper divisors of n.
- A352055 (program): Sum of the 9th powers of the divisor complements of the odd proper divisors of n.
- A352056 (program): Sum of the 10th powers of the divisor complements of the odd proper divisors of n.
- A352060 (program): a(n) = (n - 1)! * omega(n), where omega(n) = number of distinct primes dividing n (A001221).
- A352067 (program): Triangle read by rows: T(n,k) is the number of connected graphs with n nodes and degeneracy k, 0 <= k < n.
- A352115 (program): Partial sums of the even triangular numbers (A014494).
- A352149 (program): a(n) = Sum_{k=0..n-1} binomial(n,k)^2 * (n-k-1)!.
- A352150 (program): a(n) = Sum_{k=0..n-1} (-1)^k * binomial(n,k)^2 * (n-k-1)!.
- A352172 (program): a(n) is the product of the cubes of the nonzero digits of n.
- A352177 (program): a(n) is the number of symmetric Toeplitz anti-Hadamard matrices of order n whose sum of the inverse squares of their singular values is maximal.
- A352180 (program): a(n) = 9*A006190(n)+1.
- A352181 (program): a(n) = A200993(n)/2.
- A352182 (program): Twice A200994.
- A352190 (program): Indices of records in A352188.
- A352217 (program): Smallest power of 2 that is one more than a multiple of 2n-1.
- A352227 (program): Number of length-n blocks in the Thue-Morse sequence with intertwining pattern AB AB AB… .
- A352228 (program): Number of length-n blocks in the Thue-Morse sequence with intertwining pattern ABBA ABBA ABBA… .
- A352241 (program): Maximal number of nonattacking black-square queens on an n X n chessboard.
- A352257 (program): Sum of all parts of all partitions of n into an odd number of consecutive parts.
- A352447 (program): Numbers k such that BarnesG(k) is divisible by Gamma(k).
- A352598 (program): a(n) is the product of the squares of the nonzero digits of n.
- A352601 (program): a(n) = RisingFactorial(2*n, n) = A124320(2*n, n).