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%I #17 Oct 06 2017 18:32:35
%S 1,1,3,12,66,450,3510,32760,335160,3832920,48648600,673596000,
%T 9961736400,161026866000,2775402630000,50713246584000,987048958896000,
%U 20331148966128000,440625863806128000,10057578887708352000,240218186856167520000,6010719623406257760000
%N E.g.f.: Product_{m>0} 1/(1 - x^m + x^(2*m)/2!).
%H Seiichi Manyama, <a href="/A293302/b293302.txt">Table of n, a(n) for n = 0..444</a>
%t nmax = 25; CoefficientList[Series[1/Product[1 - x^k + x^(2*k)/2, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 05 2017 *)
%o (PARI) x = 'x + O('x^40); Vec(serlaplace(prod(m=1, 40, 1/(1 - x^m + x^(2m)/2!)))) \\ _Michel Marcus_, Oct 05 2017
%Y Column k=2 of A293301.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 05 2017
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