A372334 Expansion of e.g.f. -exp(x) * LambertW(-3*x)/3.

0, 1, 8, 102, 2092, 60140, 2220954, 100119670, 5328468968, 326960686872, 22724388453070, 1764411577328906, 151364204180518476, 14217940294767407380, 1451334877597451677250, 159972528561402504191190, 18936257811933773637390544, 2395818853376147403857700656

Offset: 0

Author

Seiichi Manyama, Apr 28 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..334
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A277473, A372333.

Cf. A372316.

Programs

PARI

my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-exp(x)*lambertw(-3*x)/3)))

PARI

a(n) = sum(k=1, n, (3*k)^(k-1)*binomial(n, k));

Formula

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

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

a(n) ~ exp(exp(-1)/3) * 3^(n-1) * n^(n-1). - Vaclav Kotesovec, Apr 30 2024