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A354122
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Expansion of e.g.f. 1/(1 + log(1 - x))^3.
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8
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1, 3, 15, 102, 870, 8892, 105708, 1431168, 21722136, 365105928, 6729341832, 134915992560, 2922576142320, 68013701197920, 1692075061072800, 44810389419079680, 1258472984174461440, 37357062009383877120, 1168635883239630120960, 38424619272539153157120
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (1/2) * Sum_{k=0..n} (k + 2)! * |Stirling1(n,k)|.
a(n) ~ sqrt(Pi/2) * n^(n + 5/2) / (exp(1) - 1)^(n+3). - Vaclav Kotesovec, Jun 04 2022
a(0) = 1; a(n) = Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Nov 19 2023
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PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x))^3))
(PARI) a(n) = sum(k=0, n, (k+2)!*abs(stirling(n, k, 1)))/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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