A351134 a(n) = Sum_{k=0..n} k! * k^(3*n) * Stirling1(n,k).

1, 1, 127, 115028, 383611414, 3407421330934, 66396378581670602, 2493320561997330821496, 164454446238949941359354760, 17769323863754938530919641304080, 2978930835291629440372517431365668448, 741834782450714229554166000654848368247568

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..125

Formula

E.g.f.: Sum_{k>=0} log(1 + k^3*x)^k.

a(n) ~ c * d^n * n^(4*n + 1/2), where d = 0.358437102792682941192966771107499325675345706113923587904567864366079667... and c = 2.68150179193269103258189978938660205530269361522513... - Vaclav Kotesovec, Feb 04 2022

Mathematica

a[0] = 1; a[n_] := Sum[k! * k^(3*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 12, 0] (* Amiram Eldar, Feb 02 2022 *)

Prog

(PARI) a(n) = sum(k=0, n, k!*k^(3*n)*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k^3*x)^k)))

Crossrefs

Cf. A006252, A320083, A351133.

Cf. A242229, A351135, A351137.

Sequence in context: A175825 A217914 A203798 * A195218 A215692 A212860

Adjacent sequences: A351131 A351132 A351133 * A351135 A351136 A351137

Keyword

nonn

Author

Seiichi Manyama, Feb 02 2022

Status

approved