A326863 E.g.f.: Product_{k>=1} (1 + x^(4*k-3)/(4*k-3)) / (1 - x^(4*k-3)/(4*k-3)).
1, 2, 4, 12, 48, 288, 2016, 14112, 112896, 1096704, 12063744, 135894528, 1630734336, 22157549568, 331366920192, 5107664314368, 82057393668096, 1436821272133632, 27168078863794176, 528845513033908224, 10627947138360803328, 228216184936879620096, 5219125284175176794112
Offset: 0
Keywords
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Product[(1+x^(4*k-3)/(4*k-3))/(1-x^(4*k-3)/(4*k-3)), {k, 1, Floor[nmax/4]+1}], {x, 0, nmax}], x] * Range[0, nmax]!
Formula
a(n) ~ 4 * exp(-gamma/2) * sqrt(n) * n! / Pi, where gamma is the Euler-Mascheroni constant A001620.