OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(k-1) * binomial(n,3*k)/k!.
E.g.f.: (LambertW( -3*x^3/(1-x)^3 ) / (-3*x^3))^(1/3).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^3)))/x))
(PARI) a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(n, 3*k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 03 2024
STATUS
approved