A362892 Expansion of e.g.f. 1/(1 + LambertW(-x^2 * (exp(x) - 1))).

1, 0, 0, 6, 12, 20, 1470, 10122, 47096, 1814472, 25119450, 226527950, 6732015972, 142901684796, 2071229736758, 57596022404130, 1589579741044080, 32832196825559312, 951335638952843826, 31043287459520549910, 838738470701197009820

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/3)} k^k * Stirling2(n-2*k,k)/(n-2*k)!.

Prog

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

Crossrefs

Cf. A282190, A362836.

Cf. A240989, A362891.

Sequence in context: A371116 A356949 A375827 * A371304 A355508 A371139

Adjacent sequences: A362889 A362890 A362891 * A362893 A362894 A362895

Keyword

nonn

Author

Seiichi Manyama, May 08 2023

Status

approved