A308491 a(0) = 1, a(n) = Sum_{k=1..n} stirling2(n,k) * k^(3*k).

1, 1, 65, 19876, 16895763, 30685843321, 102018812632786, 560682901512212459, 4738032814084465062121, 58320000513552476843995786, 1002620283226568243192938115197, 23280221638971518379191182864465213, 710336441472841166799952152725333251616

Offset: 0

Author

Vaclav Kotesovec, May 31 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..152

Crossrefs

Cf. A282190, A308490, A316748.

Programs

Mathematica

Join[{1}, Table[Sum[k^(3*k)*StirlingS2[n, k], {k, 1, n}], {n, 1, 15}]]

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^3*(exp(x)-1))^k/k!))) \\ Seiichi Manyama, Feb 04 2022

Formula

a(n) ~ n^(3*n).

E.g.f.: Sum_{k>=0} (k^3 * (exp(x) - 1))^k / k!. - Seiichi Manyama, Feb 04 2022