%I
%S 1,1,1,5,14,40,122,404,1362,4608,15881,55709,197402,705114,
%T 2539282,9210196,33605471,123262137,454268676,1681305246,
%U 6246544735,23288217459,87096982499,326680267261,1228547420236,4631474743422,17499462106763,66257720483935,251356773101419
%N Expansion of Product_{k>0} (1+sqrt(1+4*x^k))/(2*x^k).
%H Seiichi Manyama, <a href="/A327682/b327682.txt">Table of n, a(n) for n = 0..1000</a>
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+sqrt(1+4*x^k))/(2*x^k)))
%o (PARI) N=66; x='x+O('x^N); Vec(prod(i=1, N, sum(j=0, N\i, (1)^j*binomial(2*j, j)*x^(i*j)/(j+1))))
%Y Cf. A000108, A081362, A168491, A309867, A322204, A327683.
%K sign
%O 0,4
%A _Seiichi Manyama_, Sep 22 2019
