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Expansion of Product_{j>=1} 1/(1 - (-1 + Product_{k>=1} 1/(1 - x^k)^k)^j)^j.
3

%I #6 Apr 02 2019 19:19:21

%S 1,1,6,30,143,660,3000,13448,59696,262788,1148738,4989908,21551733,

%T 92596511,395921737,1685304092,7143861196,30163965903,126895681419,

%U 531986033218,2222961809367,9260148591001,38461580964389,159302487751844,658054630483936,2711429650817356

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

%F G.f.: g(g(x) - 1), where g(x) = g.f. of A000219 (number of planar partitions).

%t nmax = 25; CoefficientList[Series[Product[1/(1 - (-1 + Product[1/(1 - x^k)^k, {k, 1, nmax}])^j)^j, {j, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000219, A307127, A307323.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 02 2019