A355181 Expansion of e.g.f. -LambertW(x^2/2 * (1 - exp(x))).

0, 0, 0, 3, 6, 10, 195, 1281, 5908, 90756, 1098765, 9605035, 147947646, 2496239538, 33836915203, 588360763095, 12104789358600, 223722576473896, 4578806487368313, 108875473376842467, 2519418390663035170, 60831875074927797750, 1640260621340460494991

Offset: 0

Author

Seiichi Manyama, Sep 24 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A048802, A355308, A357267.

Programs

PARI

my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(serlaplace(-lambertw(x^2/2*(1-exp(x))))))

PARI

a(n) = n!*sum(k=1, n\3, k^(k-1)*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=1..floor(n/3)} k^(k-1) * Stirling2(n-2*k,k)/(2^k * (n-2*k)!).