A351182 a(n) = Sum_{k=0..n} k^(2*k) * Stirling1(n,k).

1, 1, 15, 683, 61332, 9135004, 2035708760, 634172615600, 263166948202080, 140322186951905736, 93484350581344936344, 76095870609142447018152, 74311960997497053384537408, 85748280952260853814490688656

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

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

a(n) ~ exp(-exp(-2)/2) * n^(2*n). - Vaclav Kotesovec, Feb 18 2022

Prog

(PARI) a(n) = sum(k=0, n, k^(2*k)*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*log(1+x))^k/k!)))

Crossrefs

Cf. A308490, A305819, A350721, A351180, A351183.

Sequence in context: A079600 A171113 A166186 * A266519 A177230 A209499

Adjacent sequences: A351179 A351180 A351181 * A351183 A351184 A351185

Keyword

nonn

Author

Seiichi Manyama, Feb 04 2022

Status

approved