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A305988
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Expansion of e.g.f. 1/(1 + log(2 - exp(x))).
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4
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1, 1, 4, 24, 194, 1970, 24062, 343294, 5601122, 102847794, 2098766582, 47117285270, 1154031484586, 30622256174458, 875092190716382, 26794239236959806, 875110094707912562, 30367988674208286914, 1115822099409002188358, 43276913813553367194598, 1766830322476935945014330
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Stirling2(n,k)*A007840(k).
a(n) ~ n! / ((2*exp(1) - 1) * (log(2 - exp(-1)))^(n+1)). - Vaclav Kotesovec, Jul 01 2018
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EXAMPLE
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1/(1 + log(2 - exp(x))) = 1 + x + 4*x^2/2! + 24*x^3/3! + 194*x^4/4! + 1970*x^5/5! + 24062*x^6/6! + ...
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MAPLE
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b:= proc(n) b(n):= n!*`if`(n=0, 1, add(b(k)/(k!*(n-k)), k=0..n-1)) end:
a:= n-> add(Stirling2(n, j)*b(j$2), j=0..n):
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MATHEMATICA
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nmax = 20; CoefficientList[Series[1/(1 + Log[2 - Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Sum[StirlingS2[n, k] Abs[StirlingS1[k, j]] j!, {j, 0, k}], {k, 0, n}], {n, 0, 20}]
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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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