A353200 Expansion of e.g.f. 1/(1 + log(1 - x)^5).

1, 0, 0, 0, 0, 120, 1800, 21000, 235200, 2693880, 35947800, 609615600, 12504927600, 281242996320, 6545492073120, 155873050569600, 3849612346944000, 100588974863402880, 2818516832681523840, 84728757269204858880, 2706516690047188416000

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..418

Formula

a(0) = 1; a(n) = 120 * Sum_{k=1..n} binomial(n,k) * |Stirling1(k,5)| * a(n-k).

a(n) = Sum_{k=0..floor(n/5)} (5*k)! * |Stirling1(n,5*k)|.

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (5 * (exp(1) - 1)^(n+1)). - Vaclav Kotesovec, May 07 2022

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x)^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)*abs(stirling(j, 5, 1))*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\5, (5*k)!*abs(stirling(n, 5*k, 1)));

Crossrefs

Cf. A052811, A353118, A353119.

Cf. A346924.

Sequence in context: A354232 A052767 A353404 * A110839 A219720 A346574

Adjacent sequences: A353197 A353198 A353199 * A353201 A353202 A353203

Keyword

nonn

Author

Seiichi Manyama, May 06 2022

Status

approved