A354230 Expansion of e.g.f. 1/(1 - log(1 + x)^5).

1, 0, 0, 0, 0, 120, -1800, 21000, -235200, 2693880, -28690200, 210447600, 1465952400, -123513355680, 4155643171680, -114924516470400, 2886135295680000, -66750668391381120, 1375830884058456960, -22036006671394705920, 70186623981895296000, 16180846322732941893120

Offset

0,6

Links

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

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).

Mathematica

With[{nn=30}, CoefficientList[Series[1/(1-Log[1+x]^5), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 20 2024 *)

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)*stirling(j, 5, 1)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 1));

Crossrefs

Cf. A006252, A354229.

Cf. A353200, A354135, A354232.

Sequence in context: A001118 A375773 A373940 * A354232 A052767 A353404

Adjacent sequences: A354227 A354228 A354229 * A354231 A354232 A354233

Keyword

sign

Author

Seiichi Manyama, May 20 2022

Status

approved