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Expansion of Product_{j>=1} (1 + (-1 + Product_{k>=1} (1 + x^k))^j).
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%I #5 Mar 26 2019 21:07:30

%S 1,1,2,6,15,40,103,266,683,1753,4481,11417,28993,73414,185424,467302,

%T 1175322,2950467,7393090,18492029,46173538,115102596,286482967,

%U 711990108,1767048214,4379814978,10842382074,26808912074,66212421302,163351562975,402575169429,991119918949

%N Expansion of Product_{j>=1} (1 + (-1 + Product_{k>=1} (1 + x^k))^j).

%F G.f.: q(q(x) - 1), where q(x) = g.f. of A000009 (number of partitions into distinct parts).

%t nmax = 31; CoefficientList[Series[Product[(1 + (-1 + Product[(1 + x^k), {k, 1, nmax}])^j), {j, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000009, A307127.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 26 2019