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

Author

Seiichi Manyama, May 05 2023

Keywords

• sign

Links

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

Crossrefs

Column k=3 of A362856.

Cf. A362860.

Programs

PARI

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

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).