A362858 Expansion of e.g.f. exp(-3*x) / (1 + LambertW(-x)).

1, -2, 7, -9, 121, 797, 14517, 251521, 5199313, 120881133, 3139282909, 90010844657, 2824532243001, 96284834673349, 3543187673495269, 139992580020525993, 5910844405813258273, 265606657711863337181, 12655895981349401656749

Offset

0,2

Links

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

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

Formula

G.f.: Sum_{k>=0} (k*x)^k / (1 + 3*x)^(k+1).

a(n) = Sum_{k=0..n} (-3)^(n-k) * k^k * binomial(n,k).

Prog

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

Crossrefs

Column k=3 of A362856.

Cf. A362860.

Sequence in context: A272412 A042561 A252661 * A041453 A042157 A012937

Adjacent sequences: A362855 A362856 A362857 * A362859 A362860 A362861

Keyword

sign

Author

Seiichi Manyama, May 05 2023

Status

approved