A376100 Expansion of e.g.f. -LambertW(-x / (1 - 2*x)).

0, 1, 6, 57, 760, 13265, 289116, 7600873, 234730224, 8340307137, 335388171700, 15062758093361, 747393408423432, 40606032733746961, 2397539426985311532, 152864047998089113785, 10467226142002168282336, 766094017043351707135745

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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

Formula

E.g.f. A(x) satisfies A(x) = x * (2*A(x) + exp(A(x))).

E.g.f.: Series_Reversion( x / (2*x + exp(x)) ).

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

a(n) ~ (1 + 2*exp(-1))^(n + 1/2) * n^(n-1). - Vaclav Kotesovec, Sep 10 2024

Prog

(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-x/(1-2*x)))))
(PARI) a(n) = n!*sum(k=1, n, 2^(n-k)*k^(k-1)*binomial(n-1, k-1)/k!);

Crossrefs

Cf. A052871, A376101.

Sequence in context: A032119 A294511 A242817 * A295238 A256016 A361291

Adjacent sequences: A376097 A376098 A376099 * A376101 A376102 A376103

Keyword

nonn,changed

Author

Seiichi Manyama, Sep 10 2024

Status

approved