A385011 G.f.: 1/Product_{k>=1} (1 - x^(2*k^2)) * (1 - x^k).
1, 1, 3, 4, 8, 11, 19, 26, 42, 57, 86, 116, 168, 224, 314, 415, 568, 743, 998, 1293, 1709, 2196, 2862, 3649, 4702, 5950, 7590, 9540, 12061, 15064, 18895, 23460, 29220, 36081, 44651, 54854, 67490, 82513, 100979, 122904, 149671, 181400, 219904, 265463, 320453, 385397
Offset: 0
Keywords
Programs
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Mathematica
nmax = 60; CoefficientList[Series[1/Product[(1-x^(2*k^2))*(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Formula
a(n) ~ exp(Pi*sqrt(2*n/3) + 3^(1/4)*zeta(3/2)*n^(1/4)/2^(5/4) - 3*zeta(3/2)^2/(64*Pi)) / (2^(11/4) * 3^(3/4) * sqrt(Pi) * n^(5/4)).
Comments