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A302548
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Expansion of e.g.f. -log(1 + log(1 - x))/(1 + log(1 - x)).
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5
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0, 1, 4, 22, 155, 1333, 13541, 158688, 2107682, 31291894, 513590170, 9234669420, 180534475832, 3812852144788, 86517295628188, 2099170738243328, 54233876338638192, 1486517654443664016, 43084555863325589232, 1316588795487600071904, 42306543064537291007424, 1426115146736949130634400
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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=1..n} |Stirling1(n,k)|*H(k)*k!, where H(k) is the k-th harmonic number.
a(n) ~ sqrt(2*Pi) * log(n) * n^(n + 1/2) / (exp(1)-1)^(n+1). - Vaclav Kotesovec, Jun 23 2018
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EXAMPLE
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E.g.f.: A(x) = x + 4*x^2/2! + 22*x^3/3! + 155*x^4/4! + 1333*x^5/5! + 13541*x^6/6! + ...
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MAPLE
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H:= proc(n) H(n):= 1/n +`if`(n=1, 0, H(n-1)) end:
a:= n-> add(abs(Stirling1(n, k))*H(k)*k!, k=1..n):
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MATHEMATICA
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nmax = 21; CoefficientList[Series[-Log[1 + Log[1 - x]]/(1 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] HarmonicNumber[k] k!, {k, 0, n}], {n, 0, 21}]
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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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