A374018 Expansion of Product_{k>=1} 1 / (1 - x^(3*k-1))^2.
1, 0, 2, 0, 3, 2, 4, 4, 7, 6, 13, 10, 19, 18, 27, 30, 42, 44, 63, 66, 91, 100, 130, 144, 187, 206, 263, 294, 364, 412, 506, 568, 696, 782, 943, 1070, 1273, 1444, 1713, 1936, 2285, 2586, 3027, 3428, 3996, 4516, 5243, 5924, 6841, 7730, 8895, 10030, 11512, 12966, 14825, 16696
Offset: 0
Keywords
Programs
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Mathematica
nmax = 55; CoefficientList[Series[Product[1/(1 - x^(3 k - 1))^2, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
a(0) = 1; a(n) = (2/n) * Sum_{k=1..n} A078182(k) * a(n-k).
a(n) ~ exp(2*Pi*sqrt(n)/3) * Pi^(4/3) / (3^(3/2) * Gamma(1/3)^2 * n^(11/12)). - Vaclav Kotesovec, Jun 25 2024