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Expansion of e.g.f. Product_{j>=1} 1/(1 - (-1 + Product_{k>=1} 1/(1 - x^k/k!))^j/j!).
1

%I #6 Apr 16 2019 15:27:44

%S 1,1,6,47,475,5857,85582,1442814,27569010,588533169,13880832378,

%T 358407441163,10054835359411,304540419456509,9904454527313548,

%U 344267509478109266,12736907296570957669,499767123093151036603,20730741476220960428814,906482220845570488188348,41675291255765161672107867

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

%F E.g.f.: g(g(x) - 1), where g(x) = e.g.f. of A005651.

%t nmax = 20; CoefficientList[Series[Product[1/(1 - (-1 + Product[1/(1 - x^k/k!), {k, 1, nmax}])^j/j!), {j, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A005651, A307568.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 15 2019