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

%I #20 Apr 16 2019 15:27:31

%S 1,1,6,30,145,680,3151,14394,65217,293223,1310255,5820697,25725139,

%T 113161286,495659656,2162471602,9399682398,40716499477,175798072996,

%U 756709512011,3247830724594,13901967775738,59352638426839,252778786749676,1074061758972744,4553583433874616,19264461634793094

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

%F G.f.: g(g(x) - 1), where g(x) = g.f. of A006906.

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

%Y Cf. A006906, A307127, A307321, A307566.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 15 2019