A301556 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(sigma_2(k)).

1, 2, 12, 42, 154, 498, 1640, 4990, 15092, 43840, 125220, 348478, 954294, 2561714, 6776404, 17644494, 45338734, 114971434, 288148860, 713968998, 1750662814, 4249685398, 10219662844, 24356466418, 57558783492, 134922807056, 313842321696, 724651728916

Offset: 0

Author

Vaclav Kotesovec, Mar 23 2018

Keywords

• nonn

Comments

Convolution of A275585 and A288414.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A001157, A275585, A288414.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^DivisorSigma[2, k], {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(2^(5/4) * Pi * Zeta(3)^(1/4) * n^(3/4)/3 - Pi*n^(1/4) / (3 * 2^(13/4) * Zeta(3)^(1/4)) + Zeta(3)/(8*Pi^2)) * Zeta(3)^(1/8) / (2^(15/8) * n^(5/8)).