A362704 Expansion of e.g.f. 1/(1 + LambertW(-x^2/2 * exp(x))).

1, 0, 1, 3, 18, 130, 1140, 11886, 142408, 1934640, 29357100, 492249340, 9038206056, 180352513848, 3886286296984, 89937276717120, 2224716791224320, 58577968147130176, 1635780290409117648, 48286974141713673072, 1502385897082471446880

Offset

0,4

Links

Table of n, a(n) for n=0..20.

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

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x^2/2*exp(x)))))

Crossrefs

Cf. A072034, A362705.

Cf. A362350.

Sequence in context: A171805 A368963 A154931 * A047731 A291841 A322139

Adjacent sequences: A362701 A362702 A362703 * A362705 A362706 A362707

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 30 2023

Status

approved