OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (Product_{j=0..k-1} (3*j+1)) * Stirling2(n-k,k)/(n-k)!.
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*(exp(x)-1))^(1/3)))
(PARI) a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+1)*stirling(n-k, k, 2)/(n-k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 24 2024
STATUS
approved