%I #14 Oct 15 2017 05:13:02
%S 1,1,0,6,24,120,720,5040,80640,725760,7257600,79833600,1437004800,
%T 18681062400,261534873600,5230697472000,104613949440000,
%U 1778437140480000,32011868528640000,729870602452992000,17030314057236480000,408727537373675520000,8992005822220861440000
%N E.g.f.: Product_{m>0} (1 + x^(2*m-1)).
%F a(n) = n! * A000700(n).
%F a(n) ~ sqrt(Pi) * exp(Pi*sqrt(n/6) - n) * n^(n - 1/4) / (2^(5/4) * 3^(1/4)). - _Vaclav Kotesovec_, Oct 15 2017
%t nmax = 20; CoefficientList[Series[Product[1 + x^(2*k-1), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 15 2017 *)
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(m=1, N, 1+x^(2*m-1))))
%Y Column k=1 of A293486.
%Y Cf. A000700, A293300.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Oct 10 2017