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A302547
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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, 2, 4, 11, 33, 131, 516, 2810, 12934, 97870, 447940, 5308112, 16394116, 450505844, -315178912, 60774618672, -394330113648, 12662225550288, -157622647720032, 3766647294946944, -64679214198647520, 1475157821754785184, -30431206030329719424, 719032203373502252160
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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.
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EXAMPLE
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E.g.f.: A(x) = x + 2*x^2/2! + 4*x^3/3! + 11*x^4/4! + 33*x^5/5! + 131*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(Stirling1(n, k)*H(k)*k!, k=1..n):
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MATHEMATICA
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nmax = 24; CoefficientList[Series[-Log[1 - Log[1 + x]]/(1 - Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] HarmonicNumber[k] k!, {k, 0, n}], {n, 0, 24}]
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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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