%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