A356688 a(n) = n! * Sum_{k=0..n} k^(3*n)/k!.

1, 1, 66, 21225, 18952156, 36175231585, 126556309395486, 733064060959310689, 6540867625730306094360, 85180334386943946887707617, 1552697061493449955344530003290, 38315904135534199560725372265381721, 1245605749857294018587318829355458646068

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..149

Formula

E.g.f.: Sum_{k>=0} (k^3 * x)^k / (k! * (1 - k^3 * x)).

Mathematica

a[n_] := n! * Sum[k^(3*n)/k!, {k, 0, n}]; a[0] = 1; Array[a, 13, 0] (* Amiram Eldar, Aug 23 2022 *)

Prog

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

Crossrefs

Cf. A256016, A356687.

Cf. A337001, A349901, A356673.

Sequence in context: A197439 A127706 A355470 * A167778 A199838 A188453

Adjacent sequences: A356685 A356686 A356687 * A356689 A356690 A356691

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2022

Status

approved