A305119 G.f.: Sum_{k>=1} x^k/(1-x^k) * Product_{k>=1} 1/(1-x^k)^2.
0, 1, 4, 11, 27, 58, 119, 227, 420, 744, 1287, 2160, 3561, 5739, 9113, 14224, 21924, 33327, 50126, 74531, 109802, 160211, 231875, 332821, 474313, 671072, 943411, 1317826, 1830290, 2527583, 3472446, 4746093, 6456291, 8741999, 11785768, 15822047, 21156278
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
nmax = 40; CoefficientList[Series[Sum[x^k/(1-x^k), {k, 1, nmax}] * Product[1/(1-x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
a(n) ~ exp(2*Pi*sqrt(n/3)) * (2*gamma + log(3*n/Pi^2)) / (8*3^(1/4)*Pi*n^(3/4)), where gamma is the Euler-Mascheroni constant A001620.
Comments