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Expansion of Product_{j>=1} (1 + (-1 + Product_{k>=1} (1 + x^k)^k)^j)^j.
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%I #5 Apr 02 2019 19:19:33

%S 1,1,4,18,74,303,1206,4741,18466,71463,274879,1051509,4001727,

%T 15157935,57170668,214787989,804049797,2999846236,11156943967,

%U 41370989836,152973793900,564117250793,2074959664189,7613615954760,27871659379578,101805487967357,371072295698710

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

%F G.f.: g(g(x) - 1), where g(x) = g.f. of A026007.

%t nmax = 26; CoefficientList[Series[Product[(1 + (-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^j)^j, {j, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A026007, A307128, A307321.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 02 2019