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A354135
Expansion of e.g.f. 1/(1 - log(1 + x)^5/120).
3
1, 0, 0, 0, 0, 1, -15, 175, -1960, 22449, -269073, 3403070, -45510630, 643152796, -9586136560, 150319669136, -2473024029840, 42562037379744, -764017130370276, 14260496108114340, -275877454002406236, 5512350021871343616, -113318466860425703184
OFFSET
0,7
FORMULA
a(0) = 1; a(n) = 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)/120^k.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-log(1+x)^5/120)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=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)/120^k);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 18 2022
STATUS
approved