A356687 a(n) = n! * Sum_{k=0..n} k^(2*n)/k!.

1, 1, 18, 927, 94876, 16251045, 4210190766, 1543550310211, 764096247603480, 493254380867214249, 404269328278061434810, 411862088865696890314311, 512690851568229926690616948, 768775988931240685277619894157

Offset: 0

Author

Seiichi Manyama, Aug 23 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..196

Crossrefs

Cf. A256016, A356688.

Cf. A030297, A249459, A356672.

Programs

Mathematica

a[n_] := n! * Sum[k^(2*n)/k!, {k, 0, n}]; a[0] = 1; Array[a, 14, 0] (* Amiram Eldar, Aug 23 2022 *)

PARI

a(n) = n!*sum(k=0, n, k^(2*n)/k!);

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*x)^k/(k!*(1-k^2*x)))))

Formula

E.g.f.: Sum_{k>=0} (k^2 * x)^k / (k! * (1 - k^2 * x)).