OFFSET
0,6
FORMULA
G.f.: Sum_{k>=0} (5*k)! * x^(5*k)/Product_{j=1..5*k} (1 - j * x).
a(0) = 1; a(n) = 120 * Sum_{k=1..n} binomial(n,k) * Stirling2(k,5) * a(n-k).
a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling2(n,5*k).
a(n) ~ n! / (10 * log(2)^(n+1)). - Vaclav Kotesovec, Aug 27 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x)-1)^5)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=120*sum(j=1, i, binomial(i, j)*stirling(j, 5, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 27 2024
STATUS
approved