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%I #5 Apr 10 2019 04:45:17
%S 1,1,0,2,0,5,1,9,2,17,10,26,39,22,136,-69,450,-474,1457,-1920,4543,
%T -6596,13627,-20780,39356,-61431,109448,-171688,292114,-453814,741646,
%U -1126365,1760851,-2566719,3762671,-5049452,6482765,-6806770,4649834,5114037,-30577380
%N Expansion of Product_{j>=1} 1/(1 + (-1 + Product_{k>=1} 1/(1 + x^k))^j).
%F G.f.: g(g(x) - 1), where g(x) = g.f. of A081362.
%t nmax = 40; CoefficientList[Series[Product[1/(1 + (-1 + Product[1/(1 + x^k), {k, 1, nmax}])^j), {j, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 40; CoefficientList[Series[QPochhammer[QPochhammer[x, x^2] - 1, (QPochhammer[x, x^2] - 1)^2], {x, 0, nmax}], x]
%Y Cf. A081362, A306456, A307127, A307128.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Apr 08 2019