A301873 Expansion of Product_{k>=1} 1/(1 - x^k)^A007437(k).

1, 1, 5, 12, 36, 80, 215, 476, 1154, 2539, 5772, 12417, 27146, 57111, 120822, 249389, 514201, 1041684, 2103211, 4189502, 8306632, 16296337, 31803839, 61530913, 118413823, 226200319, 429857982, 811633548, 1524828119, 2848379512, 5295550209

Offset: 0

Author

Vaclav Kotesovec, Mar 28 2018

Keywords

• nonn

Comments

Euler transform of A007437.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007437, A301874.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[Sum[(DivisorSigma[1, k] + DivisorSigma[2, k]) * x^(j*k) / (2*j), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)

Formula

a(n) ~ exp(2^(7/4) * Pi * Zeta(3)^(1/4) * n^(3/4) / (3^(5/4) * 5^(1/4)) + sqrt(5*Zeta(3)*n/6)/2 - (7*Pi * 5^(1/4) / (2^(15/4) * 3^(7/4) * Zeta(3)^(1/4)) + 5^(5/4) * Zeta(3)^(3/4) / (2^(15/4) * 3^(3/4) * Pi)) * n^(1/4) + (17*Zeta(3))/(72*Pi^2) + 23/576) * A^(1/4) * Zeta(3)^(23/192) / (2^(307/192) * 15^(23/192) * n^(119/192)), where A is the Glaisher-Kinkelin constant A074962.