A351504 Expansion of e.g.f. 1/(1 + x^3 * log(1 - x)).
1, 0, 0, 0, 24, 60, 240, 1260, 48384, 423360, 3844800, 38253600, 896797440, 14322147840, 216997522560, 3350656108800, 74820944056320, 1621271286835200, 34293811249152000, 727304513980262400, 18147791755697356800, 476653146551318016000
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..436
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^3*log(1-x)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=4, i, 1/(j-3)*v[i-j+1]/(i-j)!)); v;
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PARI
a(n) = n!*sum(k=0, n\4, k!*abs(stirling(n-3*k, k, 1))/(n-3*k)!);
Formula
a(0) = 1; a(n) = n! * Sum_{k=4..n} 1/(k-3) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/4)} k! * |Stirling1(n-3*k,k)|/(n-3*k)!.