A362860 Expansion of e.g.f. exp(-x) / (1 + LambertW(-3*x)).

1, 2, 31, 629, 18025, 662639, 29752957, 1578248867, 96577834801, 6696994946543, 518978239136341, 44448540938239811, 4169223860364566857, 425060509005908328071, 46801425208023247277965, 5534686715620432932442619, 699654866766940182167273185

Offset

0,2

Links

Table of n, a(n) for n=0..16.

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

Formula

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

a(n) = (-1)^n * Sum_{k=0..n} (-3*k)^k * binomial(n,k).

Prog

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

Crossrefs

Column k=3 of A362019.

Cf. A091482, A362858.

Sequence in context: A071360 A108491 A088104 * A057692 A058244 A245051

Adjacent sequences: A362857 A362858 A362859 * A362861 A362862 A362863

Keyword

nonn,easy

Author

Seiichi Manyama, May 05 2023

Status

approved