A362836 Expansion of e.g.f. 1/(1 + LambertW(-x * (exp(x) - 1))).

1, 0, 2, 3, 52, 245, 4086, 36547, 663832, 8984313, 184262770, 3334315391, 77900601780, 1751855308645, 46508427942718, 1241853335819475, 37195023972070576, 1144511291020453361, 38337497638919397738, 1331709923436162817447

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} k^k * Stirling2(n-k,k)/(n-k)!.

Prog

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

Crossrefs

Cf. A290158, A362835.

Sequence in context: A126716 A355648 A347894 * A375696 A371142 A337057

Adjacent sequences: A362833 A362834 A362835 * A362837 A362838 A362839

Keyword

nonn

Author

Seiichi Manyama, May 05 2023

Status

approved