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

Author

Seiichi Manyama, Sep 24 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A048802, A355179, A357267.

Programs

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;

Formula

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