A301546 Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_8(k)).

1, 1, 258, 6820, 105766, 2182826, 45173473, 800612809, 13879861574, 241973744859, 4071054739686, 66245877049645, 1059457994097088, 16655445770672940, 256617914952467489, 3883513723831505532, 57872822529451093718, 849759474364551701693, 12298914986733768863591

Offset: 0

Author

Vaclav Kotesovec, Mar 23 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1169

Crossrefs

Cf. A013956, A301552.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[1/(1-x^k)^DivisorSigma[8, k], {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(10 * 2^(7/10) * Pi * (Zeta(9)/33)^(1/10) * n^(9/10)/9 + Pi * (11/Zeta(9))^(1/10) * n^(1/10) / (480 * 2^(7/10) * 3^(9/10)) - 315*Zeta(9) / (8*Pi^8)) * (Zeta(9)/33)^(1/20) / (2^(13/20) * sqrt(5) * n^(11/20)).

G.f.: exp(Sum_{k>=1} sigma_9(k)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Oct 26 2018