A376710 G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} 1/(1 - x^j)^4.
1, 1, 4, 11, 24, 49, 93, 173, 310, 549, 946, 1608, 2676, 4391, 7083, 11283, 17724, 27539, 42309, 64382, 97052, 145092, 215161, 316737, 462980, 672310, 970154, 1391667, 1984999, 2816059, 3974475, 5581789, 7802161, 10856466, 15040941, 20751416, 28515375, 39033040
Offset: 0
Keywords
Programs
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Mathematica
nmax = 40; CoefficientList[Series[Sum[x^(k*(k+1)/2)/Product[1-x^j, {j, 1, k}]^4, {k, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
Formula
a(n) ~ r^(1/8) * (log(r)^2 + 8*polylog(2, 1-r)) * exp(sqrt(2*(log(r)^2 + 8*polylog(2, 1-r))*n)) / (2^(7/2) * Pi^2 * sqrt(1 + 3*r) * n^(3/2)), where r = 0.2755080409994... is the smallest real root of the equation r = (1-r)^4.