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

Author

Seiichi Manyama, May 05 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Column k=3 of A362019.

Cf. A091482, A362858.

Programs

PARI

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

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).