OFFSET
0,3
FORMULA
a(n) = (n!/(n+1)) * Sum_{k=0..floor(n/3)} (n-3*k)^k * binomial(n+1,n-3*k)/(6^k * k!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x*exp(x^3/6)))/x))
(PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(n+1, n-3*k)/(6^k*k!))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 05 2024
STATUS
approved