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A189423
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Expansion of e.g.f. exp(log(1+x) + log(1+x)^2).
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2
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1, 1, 2, 0, 10, -50, 368, -3052, 28740, -302220, 3508152, -44532048, 613399752, -9109006920, 145029146208, -2463935369040, 44482964644368, -850291412311152, 17153458120885152, -364163960169826944, 8114899768747511712
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OFFSET
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0,3
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LINKS
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FORMULA
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a(0) = 1; a(n) = Sum_{m=1..n} Sum_{k=m..n} k!*binomial(m,k-m)*stirling1(n,k))/m! for n>0.
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PROG
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(Maxima)
a(n):=sum(sum(k!*binomial(m, k-m)*stirling1(n, k), k, m, n)/m!, m, 1, n);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1+x)*(1+log(1+x))))) \\ Seiichi Manyama, May 14 2022
(PARI) a(n) = sum(k=0, n, k!*sum(j=0, k\2, 1/(j!*(k-2*j)!))*stirling(n, k, 1)); \\ Seiichi Manyama, May 14 2022
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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