OFFSET
0,5
FORMULA
a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+2)) * Stirling2(n-3*k,k)/(6^k*(n-3k)!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*(exp(x)-1))^(1/3)))
(PARI) a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+2)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2024
STATUS
approved