A355180 Expansion of e.g.f. -LambertW(x^3 * (1 - exp(x)))/6.

0, 0, 0, 0, 4, 10, 20, 35, 6776, 60564, 352920, 1663365, 126625180, 2361079006, 27334747804, 245495250455, 11174333090480, 328952158255400, 6245314009946736, 90576650639967369, 3209305759254634740, 122557203047084965810, 3365068665450300234580

Offset

0,5

Links

Table of n, a(n) for n=0..22.

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

Formula

a(n) = (n!/6) * Sum_{k=1..floor(n/4)} k^(k-1) * Stirling2(n-3*k,k)/(n-3*k)!.

Prog

(PARI) my(N=20, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(-lambertw(x^3*(1-exp(x)))/6)))
(PARI) a(n) = n!*sum(k=1, n\4, k^(k-1)*stirling(n-3*k, k, 2)/(n-3*k)!)/6;

Crossrefs

Cf. A048802, A355179, A357267.

Sequence in context: A356963 A375716 A370992 * A341656 A008112 A301153

Adjacent sequences: A355177 A355178 A355179 * A355181 A355182 A355183

Keyword

nonn

Author

Seiichi Manyama, Sep 24 2022

Status

approved