A376854 G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} ((1 + x^j)/(1 - x^j))^2.
1, 1, 4, 8, 13, 20, 32, 52, 84, 133, 204, 304, 444, 636, 900, 1264, 1761, 2440, 3364, 4608, 6276, 8496, 11424, 15268, 20284, 26789, 35196, 46016, 59884, 77612, 100204, 128900, 165260, 211200, 269072, 341792, 432917, 546788, 688728, 865200, 1084048, 1354816, 1689048
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Programs
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Mathematica
nmax = 60; CoefficientList[Series[Sum[x^(k^2) * Product[(1+x^j)/(1-x^j), {j, 1, k}]^2, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
Formula
a(n) ~ (1 + sqrt(2)) * exp(Pi*sqrt(n)) / (2^(9/2) * n).