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Search: id:A118051
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| A118051 |
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Denominators of coefficients in a series for the inverse of harmonic number H(x). |
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+0
4
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| 1, 24, 640, 580608, 199065600, 504627200, 2191186722816000, 44497945755648000, 255806104666112, 15953645581139831685120000, 188420950968830433165312000000, 401521614736326656000000
(list; graph; listen)
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OFFSET
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0,2
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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[Denominator[coeffs[[2i - 1]]], {i, 1, n}]
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CROSSREFS
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Numerators given in A118050. See also A002387.
Sequence in context: A126153 A002553 A006201 this_sequence A093456 A105187 A062313
Adjacent sequences: A118048 A118049 A118050 this_sequence A118052 A118053 A118054
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KEYWORD
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frac,nonn
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AUTHOR
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David W. Cantrell (DWCantrell(AT)sigmaxi.net), Apr 08 2006
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