A294668 Expansion of Product_{k>=1} 1/(1 - x^(2*k-1))^(k*(3*k+1)/2).
1, 2, 3, 11, 19, 42, 93, 170, 352, 658, 1266, 2351, 4316, 7926, 14146, 25458, 44748, 78687, 136747, 235988, 405139, 689108, 1168260, 1963940, 3289950, 5474700, 9070976, 14954802, 24537752, 40099905, 65225553, 105713691, 170600344, 274367688, 439568770, 701867457
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
Programs
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Mathematica
nmax = 50; CoefficientList[Series[Product[1/(1 - x^(2*k-1))^(k*(3*k+1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
Formula
a(n) ~ exp(2*Pi * n^(3/4) / (3*5^(1/4)) + 2*Zeta(3) * sqrt(5*n) / Pi^2 + 5^(1/4)*(5*Pi/48 - 20*Zeta(3)^2 / Pi^5) * n^(1/4) + 800 * Zeta(3)^3 / (3*Pi^8) - 73*Zeta(3) / (96*Pi^2) - 1/12) * A / (2^(115/48) * 5^(5/48) * Pi^(1/12) * n^(29/48)), where A is the Glaisher-Kinkelin constant A074962.