A362699 Expansion of e.g.f. 1/(1 + LambertW(-x * exp(x^3))).

1, 1, 4, 27, 280, 3605, 56376, 1041103, 22188496, 535856553, 14460919120, 431287416131, 14087063106216, 500112706900573, 19174548699128200, 789598137339356535, 34757031591555021856, 1628640121039415039057, 80938770039259919191584

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k)^(n-2*k) / (k! * (n-3*k)!).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x*exp(x^3)))))

Crossrefs

Cf. A072034, A362604.

Sequence in context: A194787 A020558 A259485 * A193467 A357174 A377811

Adjacent sequences: A362696 A362697 A362698 * A362700 A362701 A362702

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 30 2023

Status

approved