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%I #6 Apr 16 2019 15:27:53
%S 1,1,2,11,53,367,2680,22794,216830,2325825,27553582,351008143,
%T 4810073427,70013351163,1082415831294,17747223519590,308327844386251,
%U 5667992273930453,109909795136025124,2239594732588547820,47747134765967675665,1060822117856654685661,24480836958809924299702
%N Expansion of e.g.f. Product_{j>=1} (1 + (-1 + Product_{k>=1} (1 + x^k/k!))^j/j!).
%F E.g.f.: g(g(x) - 1), where g(x) = e.g.f. of A007837.
%t nmax = 22; CoefficientList[Series[Product[(1 + (-1 + Product[(1 + x^k/k!), {k, 1, nmax}])^j/j!), {j, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A007837, A307567.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 15 2019
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