A362891 Expansion of e.g.f. 1/(1 + LambertW(x^2 * log(1-x))).

1, 0, 0, 6, 12, 40, 1620, 11088, 80640, 2289600, 30471840, 374663520, 9819817920, 195106129920, 3507260492736, 95860364846400, 2466492401318400, 58909563259223040, 1775000008437557760, 54856736708999339520, 1629826915777548364800

Offset: 0

Author

Seiichi Manyama, May 08 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A305981, A362835.

Cf. A353228, A362892.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(x^2*log(1-x)))))

Formula

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