A118051 Denominators of coefficients in a series for the inverse of harmonic number H(x).

1, 24, 640, 580608, 199065600, 504627200, 2191186722816000, 44497945755648000, 255806104666112, 15953645581139831685120000, 188420950968830433165312000000, 401521614736326656000000

Offset: 0

Author

David W. Cantrell (DWCantrell(AT)sigmaxi.net), Apr 08 2006

Keywords

• frac
• nonn

Examples

			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.
		

Links

• David W. Cantrell, Inverse of Harmonic Numbers

Crossrefs

Numerators given in A118050. See also A002387.

Programs

Mathematica

n = 12; coeffs = InverseSeries[Exp[Series[HarmonicNumber[x - 1/2], {x, Infinity, 2n - 1}] - EulerGamma]][[3]]; Table[Denominator[coeffs[[2i - 1]]], {i, 1, n}]