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%I #20 Oct 29 2020 20:37:02
%S 1,1,1,0,-1,1,-1,-43,1831,949,-137309,-85511,3404045159,777985057,
%T -21024051077,-2192231411,467347169033357,10187765700589,
%U -11741590582705819219,-3086703970985605357,169597995722575162268081,19606186988235984155519,-62715098968866173387571821
%N 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.
%H Chao-Ping Chen, <a href="http://dx.doi.org/10.1007/s11139-015-9670-3">On the coefficients of asymptotic expansion for the harmonic number by Ramanujan</a>, The Ramanujan Journal, 40:2 (2016), 279-290. See Eq. (2.11).
%t Numerator[CoefficientList[Series[Exp[2*(HarmonicNumber[k] - EulerGamma)]/k^2, {k, Infinity, 25}], 1/k]] (* _Vaclav Kotesovec_, Feb 10 2020 *)
%Y Denominators are in A331778.
%Y Cf. A001008, A001620, A002805, A093334, A238813, A331943.
%K sign,frac
%O 0,8
%A _N. J. A. Sloane_, Feb 09 2020
%E Sign of a(7) corrected and more terms from _Vaclav Kotesovec_, Feb 10 2020
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