%I #11 Apr 23 2018 04:13:09
%S 1,4,12,52,156,612,2028,7892,27324,107396,384844,1520436,5566876,
%T 22069796,81990252,325707348,1222582268,4862950020,18395472460,
%U 73233825524,278700724764,1110232691108,4245596648876,16920914168148,64963831455996,259012955299396
%N Expansion of Product_{k>=1} ((1 + 4*x^k) / (1 - 4*x^k))^(1/2).
%F a(n) ~ sqrt(c) * 4^n / sqrt(Pi*n), where c = QPochhammer[-1, 1/4]/QPochhammer[1/4] = 3.9385207073365388638943873939345313401323799...
%t nmax = 30; CoefficientList[Series[Product[((1+4*x^k)/(1-4*x^k))^(1/2), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 30; CoefficientList[Series[(-3*QPochhammer[-4, x] / (5*QPochhammer[4, x]))^(1/2), {x, 0, nmax}], x]
%Y Cf. A261568, A246936, A067855, A303350, A303391, A303360.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Apr 23 2018