A331778 Denominators 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, 3, 1, 90, 90, 567, 5670, 340200, 113400, 11226600, 5613300, 91945854000, 18389170800, 137918781000, 13135122000, 562708626480000, 11483849520000, 2020686677689680000, 505171669422420000, 3334133018187972000000, 370459224243108000000, 115027589127485034000000

Offset: 0

Author

N. J. A. Sloane, Feb 09 2020

Keywords

• nonn
• 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

Numerators are in A331777.

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

Programs

Mathematica

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

Extensions

More terms from Vaclav Kotesovec, Feb 10 2020