OFFSET
0,2
FORMULA
E.g.f.: 1/(1 - 3*x*exp(x)).
a(n) = n! * Sum_{k=0..n} 3^(n-k) * (n-k)^k/k!.
a(0) = 1 and a(n) = 3 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
a(n) ~ n! / ((1 + LambertW(1/3)) * LambertW(1/3)^n). - Vaclav Kotesovec, Feb 19 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*exp(x))))
(PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*(n-k)^k/k!);
(PARI) a(n) = if(n==0, 1, 3*n*sum(k=0, n-1, binomial(n-1, k)*a(k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 18 2022
STATUS
approved