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A306038
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Expansion of e.g.f. (1 + x)/(1 - log(1 + x)).
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1
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1, 2, 3, 5, 12, 34, 122, 482, 2328, 11640, 71952, 424368, 3312240, 21357504, 217045488, 1351338864, 19990187520, 89379824256, 2631270916224, 892036259712, 507945420198144, -3068802187635456, 142961233091051520, -1849617314640322560, 55640352746480440320
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Stirling1(n,k)*A000522(k).
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EXAMPLE
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(1 + x)/(1 - log(1 + x)) = 1 + 2*x + 3*x^2/2! + 5*x^3/3! + 12*x^4/4! + 34*x^5/5! + 122*x^6/6! + ...
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MAPLE
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S:= series((1+x)/(1-log(1+x)), x, 51):
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MATHEMATICA
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nmax = 24; CoefficientList[Series[(1 + x)/(1 - Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!
FullSimplify[Table[Sum[StirlingS1[n, k] E Gamma[1 + k, 1], {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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