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%I #10 Jul 27 2019 08:57:30
%S 1,1,12,300,15960,1232280,157006080,25418352960,5859886032000,
%T 1655203620470400,604893737678630400,261278195494386470400,
%U 140231830875916632652800,86107922772424330377600000,63316800257542340301112320000,52666943508290765740968161280000
%N E.g.f.: 1/Product_{k>0} (1 - x^(2*k)/(2*k)) (even powers only).
%H Seiichi Manyama, <a href="/A309319/b309319.txt">Table of n, a(n) for n = 0..225</a>
%H D. H. Lehmer, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa21/aa21123.pdf">On reciprocally weighted partitions</a>, Acta Arithmetica XXI (1972), 379-388 (Theorem 6).
%F a(n) ~ exp(-gamma/2) * (2*n)! / sqrt(n) [Lehmer, 1972], where gamma is the Euler-Mascheroni constant A001620.
%t nmax = 20; Table[(CoefficientList[Series[1/Product[(1 - x^(2*k)/(2*k)), {k, 1, 2*nmax}], {x, 0, 2*nmax}], x]*Range[0, 2*nmax]!)[[2 n + 1]], {n, 0, nmax}]
%Y Cf. A007838, A007841, A087639, A088994, A294506.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jul 23 2019
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