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%I #18 May 06 2021 03:50:58
%S 1,1,0,4,-4,11,-13,39,-73,144,-256,559,-1116,2188,-4317,8804,-17591,
%T 34992,-69815,140097,-280416,560077,-1119327,2240719,-4482527,8961129,
%U -17920037,35847885,-71699202,143384383,-286760131,573549105,-1147115913,2294173485,-4588309651,9176739373
%N Expansion of Product_{k>0} (1 + x^k/(1 + x^k/(1 + x^k))).
%H Seiichi Manyama, <a href="/A327684/b327684.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ -(-1)^n * c * 2^n, where c = 1/4 * Product_{k>=2} (1 + (-1/2)^k/(1 + (-1/2)^k/(1 + (-1/2)^k))) = 0.267077782295890034289082591596560646781284184591415208072736792505213482... - _Vaclav Kotesovec_, May 06 2021
%t m = 35; CoefficientList[Series[Product[(1 + x^k/(1 + x^k/(1 + x^k))), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 06 2021 *)
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1+3*x^k+x^(2*k))/(1+2*x^k)))
%Y Cf. A000009, A268498, A327683.
%K sign
%O 0,4
%A _Seiichi Manyama_, Sep 22 2019
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