OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..334
Eric Weisstein's World of Mathematics, Lambert W-Function.
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
PROG
(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));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 28 2024
STATUS
approved