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%I #18 Jul 24 2019 07:45:44
%S 1,1,2,8,32,184,1184,9008,74752,726528,7583232,87931392,1092516864,
%T 14863589376,215094226944,3358032635904,55181218873344,
%U 970561417248768,17945595514847232,351221170194874368,7186120683011702784,155103171658691641344
%N E.g.f.: 1/Product_{k>0} (1-x^(2*k-1)/(2*k-1)).
%H Seiichi Manyama, <a href="/A294506/b294506.txt">Table of n, a(n) for n = 0..449</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 5).
%F a(n) ~ 2*exp(-gamma/2) * sqrt(2*n) * n! / Pi, where gamma is the Euler-Mascheroni constant A001620 [Lehmer, 1972]. - _Vaclav Kotesovec_, Jul 23 2019
%t nmax = 30; CoefficientList[Series[1/Product[(1-x^(2*k-1)/(2*k-1)), {k, 1, Floor[nmax/2] + 1}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Nov 02 2017 *)
%Y Cf. A007838, A007841, A087639, A088994, A309319.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 01 2017
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