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

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..415

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

Formula

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

a(n) ~ c * n^n / (exp(n) * r^n), where r = 0.6181555791782259971637080007872096609874188426179... is the root of the equation r^2 * log(1-r) = -exp(-1) and c = 1/(sqrt(2 + exp(1)*r^3/(1-r))) = 0.5211785827965928757153122972617182789149... - Vaclav Kotesovec, Jan 25 2026

Prog

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

Crossrefs

Cf. A305981, A362835, A391377.

Cf. A353228, A362892.

Sequence in context: A371118 A355287 A375826 * A371302 A371233 A356970

Adjacent sequences: A362888 A362889 A362890 * A362892 A362893 A362894

Keyword

nonn

Author

Seiichi Manyama, May 08 2023

Status

approved