A331777 Numerators of coefficients in asymptotic expansion of exp(2*(H_k-gamma))/k^2 in powers of 1/k, where H_k are the harmonic numbers A001008/A002805 and gamma is the Euler-Mascheroni constant A001620.

1, 1, 1, 0, -1, 1, -1, -43, 1831, 949, -137309, -85511, 3404045159, 777985057, -21024051077, -2192231411, 467347169033357, 10187765700589, -11741590582705819219, -3086703970985605357, 169597995722575162268081, 19606186988235984155519, -62715098968866173387571821

Offset: 0

Author

N. J. A. Sloane, Feb 09 2020

Keywords

• sign
• frac

Links

• Chao-Ping Chen, On the coefficients of asymptotic expansion for the harmonic number by Ramanujan, The Ramanujan Journal, 40:2 (2016), 279-290. See Eq. (2.11).

Crossrefs

Denominators are in A331778.

Cf. A001008, A001620, A002805, A093334, A238813, A331943.

Programs

Mathematica

Numerator[CoefficientList[Series[Exp[2*(HarmonicNumber[k] - EulerGamma)]/k^2, {k, Infinity, 25}], 1/k]] (* Vaclav Kotesovec, Feb 10 2020 *)

Extensions

Sign of a(7) corrected and more terms from Vaclav Kotesovec, Feb 10 2020