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

0,3

Links

Table of n, a(n) for n=0..22.

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).

Mathematica

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

Crossrefs

Numerators are in A331777.

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

Sequence in context: A012854 A370331 A370431 * A241191 A352232 A221195

Adjacent sequences: A331775 A331776 A331777 * A331779 A331780 A331781

Keyword

nonn,frac

Author

N. J. A. Sloane, Feb 09 2020

Extensions

More terms from Vaclav Kotesovec, Feb 10 2020

Status

approved