A375799 Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2).

1, 1, 2, 6, 36, 240, 1800, 16800, 178080, 2086560, 27518400, 399168000, 6286896000, 107623676160, 1984274772480, 39143052748800, 824445099878400, 18450791322163200, 437015358530150400, 10929450232744243200, 287728555881102336000, 7952251084537503744000

Offset: 0

Author

Seiichi Manyama, Aug 29 2024

Keywords

• nonn

Crossrefs

Cf. A007840, A375798.

Cf. A353223.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)))

PARI

a(n) = n!*sum(k=0, n\3, (n-3*k)!*abs(stirling(n-2*k, n-3*k, 1))/(n-2*k)!);

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)! * |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.