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A354230
Expansion of e.g.f. 1/(1 - log(1 + x)^5).
2
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
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).
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 20 2022
STATUS
approved

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Last modified September 20 06:31 EDT 2024. Contains 376054 sequences. (Running on oeis4.)