A118050 Numerators of coefficients in a series for the inverse of harmonic number H(x).

1, -1, 3, -1525, 615881, -3058641, 38800188510523, -3213747182969063, 100462329712125, -43865443313064357090353257, 4543042335221166932765440567147, -103986681387361620043171941

Offset: 0

Author

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

Keywords

• frac
• sign

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

Denominators given in A118051. See also A002387.

Programs

Mathematica

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