A308400 Expansion of 1 / Sum_{k=-oo..oo} (-x)^(k*(6*k + 1)).
1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 3, 0, 3, 1, 1, 3, 0, 6, 1, 3, 3, 1, 8, 1, 8, 3, 3, 9, 2, 14, 3, 9, 9, 4, 19, 4, 19, 9, 10, 21, 6, 32, 10, 22, 22, 12, 42, 12, 43, 23, 25, 48, 18, 67, 25, 51, 51, 31, 88, 31, 90, 54, 59, 101, 44, 137, 60, 108, 109, 73, 177, 73
Offset: 0
Keywords
Programs
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Mathematica
nmax = 78; CoefficientList[Series[1/Sum[(-x)^(k (6 k + 1)), {k, -nmax, nmax}], {x, 0, nmax}], x] nmax = 78; CoefficientList[Series[Product[1/((1 - x^(12 k - 7)) * (1 - x^(12 k - 5)) * (1 - x^(12 k))), {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: 1 / Sum_{k>=1} (-x)^A036498(k).
G.f.: Product_{k>=1} 1 / ((1 - x^(12*k - 7)) * (1 - x^(12*k - 5)) * (1 - x^(12*k))).
a(n) ~ (sqrt(3) - 1) * exp(sqrt(n/6)*Pi) / (2^(5/2)*n). - Vaclav Kotesovec, May 25 2019
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