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A320082
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Expansion of e.g.f. Sum_{k>=0} log(1 + k*x)^k/k!.
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5
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1, 1, 3, 5, -60, -186, 13832, -98862, -8631360, 352796880, 4245955032, -1185349047048, 48595690153920, 3201334718188320, -607575977909763840, 26489851912606455504, 4482546578798646251520, -958939334596403708474880, 50300999315063602037775360, 14223928928980522264922223360, -3933112779003946549567400925696
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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(n) = Sum_{k=0..n} Stirling1(n,k)*k^n.
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MAPLE
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1, seq(n!*coeff(series(add(log(1+k*x)^k/k!, k=1..100), x=0, 21), x, n), n=1..20); # Paolo P. Lava, Jan 09 2019
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MATHEMATICA
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nmax = 20; CoefficientList[Series[1 + Sum[Log[1 + k x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[Sum[StirlingS1[n, k] k^n, {k, n}], {n, 20}]]
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PROG
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(PARI) a(n) = sum(k=0, n, stirling(n, k)*k^n); \\ Altug Alkan, Oct 05 2018
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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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