This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309319 #10 Jul 27 2019 08:57:30
%S A309319 1,1,12,300,15960,1232280,157006080,25418352960,5859886032000,
%T A309319 1655203620470400,604893737678630400,261278195494386470400,
%U A309319 140231830875916632652800,86107922772424330377600000,63316800257542340301112320000,52666943508290765740968161280000
%N A309319 E.g.f.: 1/Product_{k>0} (1 - x^(2*k)/(2*k)) (even powers only).
%H A309319 Seiichi Manyama, <a href="/A309319/b309319.txt">Table of n, a(n) for n = 0..225</a>
%H A309319 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 A309319 a(n) ~ exp(-gamma/2) * (2*n)! / sqrt(n) [Lehmer, 1972], where gamma is the Euler-Mascheroni constant A001620.
%t A309319 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 A309319 Cf. A007838, A007841, A087639, A088994, A294506.
%K A309319 nonn
%O A309319 0,3
%A A309319 _Vaclav Kotesovec_, Jul 23 2019