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A373940
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Expansion of e.g.f. 1/(1 - (exp(x) - 1)^5).
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1
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1, 0, 0, 0, 0, 120, 1800, 16800, 126000, 834120, 8731800, 229191600, 6352632000, 143603580120, 2736395461800, 47283190718400, 860150574738000, 20236134851478120, 614854122909391800, 19930647062659477200, 615406024970593164000, 17883373100352330768120
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OFFSET
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0,6
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} (5*k)! * x^(5*k)/Product_{j=1..5*k} (1 - j * x).
a(0) = 1; a(n) = 120 * Sum_{k=1..n} binomial(n,k) * Stirling2(k,5) * a(n-k).
a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling2(n,5*k).
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x)-1)^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, 2)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 2));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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