A373940 Expansion of e.g.f. 1/(1 - (exp(x) - 1)^5).

1, 0, 0, 0, 0, 120, 1800, 16800, 126000, 834120, 8731800, 229191600, 6352632000, 143603580120, 2736395461800, 47283190718400, 860150574738000, 20236134851478120, 614854122909391800, 19930647062659477200, 615406024970593164000, 17883373100352330768120

Offset

0,6

Links

Table of n, a(n) for n=0..21.

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

Cf. A000670, A052841, A353774, A353775.

Cf. A353200.

Sequence in context: A056270 A001118 A375773 * A354230 A354232 A052767

Adjacent sequences: A373937 A373938 A373939 * A373941 A373942 A373943

Keyword

nonn

Author

Seiichi Manyama, Aug 27 2024

Status

approved