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%I #15 Oct 11 2017 05:42:50
%S 1,1,1,6,24,180,1080,10080,90720,907200,10886400,139708800,2035756800,
%T 29578348800,479480601600,7846046208000,146459529216000,
%U 2845499424768000,58421660064768000,1246862279190528000,28586598596075520000,664182248232222720000
%N E.g.f.: Product_{m>0} (1 + x^(2*m-1) + x^(4*m-2)/2!).
%H Seiichi Manyama, <a href="/A293488/b293488.txt">Table of n, a(n) for n = 0..446</a>
%F a(n) ~ 2^(-3/4) * c^(1/4) * exp(sqrt(2*c*n) - n) * n^(n-1/4), where c = -polylog(2, -1/2 - I/2) - polylog(2, -1/2 + I/2) = 0.966945612722157030083754546059357521... - _Vaclav Kotesovec_, Oct 11 2017
%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(m=1, N, 1+x^(2*m-1)+x^(4*m-2)/2)))
%Y Column k=2 of A293486.
%Y Cf. A293138, A293304.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Oct 10 2017