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%I #7 Jan 11 2020 11:45:05
%S 1,0,0,4,0,0,160,1440,0,26880,691200,7257600,11827200,395366400,
%T 14125363200,185119334400,442810368000,24049778688000,919255538073600,
%U 13662913904640000,54833495408640000,3627817738960896000,142917996623560704000,2442221696292618240000
%N E.g.f.: Product_{k>=1} (1 + x^(4*k-1)/(4*k-1)) / (1 - x^(4*k-1)/(4*k-1)).
%H Vaclav Kotesovec, <a href="/A326862/b326862.txt">Table of n, a(n) for n = 0..400</a>
%F a(n) ~ exp(-gamma/2) * n! / (2*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620.
%t nmax = 30; CoefficientList[Series[Product[(1+x^(4*k-1)/(4*k-1))/(1-x^(4*k-1)/(4*k-1)), {k, 1, Floor[nmax/4]+1}], {x, 0, nmax}], x] * Range[0, nmax]!
%Y Cf. A326855, A326779.
%Y Cf. A305199, A326859, A326860, A326863.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Jul 27 2019
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