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Search: id:A118050
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| A118050 |
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Numerators of coefficients in a series for the inverse of harmonic number H(x). |
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+0
4
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| 1, -1, 3, -1525, 615881, -3058641, 38800188510523, -3213747182969063, 100462329712125, -43865443313064357090353257, 4543042335221166932765440567147, -103986681387361620043171941
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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David W. Cantrell, Inverse of Harmonic Numbers
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EXAMPLE
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With InvH(x) being the inverse of H(x), x > 0, an asymptotic series for InvH(x) + 1/2 is u - 1/(24u) + 3/(640u^3) - 1525/(580608u^5) +-... where u = e^(x - g) and g is Euler's gamma constant.
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MATHEMATICA
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n = 12; coeffs = InverseSeries[Exp[Series[HarmonicNumber[x - 1/2], {x, Infinity, 2n - 1}] - EulerGamma]][[3]]; Table[Numerator[coeffs[[2i - 1]]], {i, 1, n}]
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CROSSREFS
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Denominators given in A118051. See also A002387.
Sequence in context: A036066 A060307 A119111 this_sequence A116994 A096730 A024047
Adjacent sequences: A118047 A118048 A118049 this_sequence A118051 A118052 A118053
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KEYWORD
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frac,sign
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AUTHOR
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David W. Cantrell (DWCantrell(AT)sigmaxi.net), Apr 08 2006
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