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A285616 Triangle read by rows: T(n,k) is the number of hypergraphs on n labeled vertices with exactly k connected components, n>=1, 1<=k<=n.

%I A285616 #10 Apr 22 2017 23:22:49
%S A285616 2,4,4,96,24,8,31840,816,96,16,2147156736,322240,4320,320,32,
%T A285616 9223372011084915712,25767883392,1957440,18240,960,64,
%U A285616 170141183460469231602560095199828453376,129127208335656968192,180389362944,9251200,67200,2688,128
%N A285616 Triangle read by rows: T(n,k) is the number of hypergraphs on n labeled vertices with exactly k connected components, n>=1, 1<=k<=n.
%F A285616 E.g.f.: A(x)^y where A(x) = Sum_{n>=0} 2^(2^n-1)x^n/n!.
%e A285616 Triangle begins:
%e A285616 2,
%e A285616 4, 4,
%e A285616 96, 24, 8,
%e A285616 31840, 816, 96, 16,
%e A285616 2147156736, 322240, 4320, 320, 32,
%e A285616 9223372011084915712, 25767883392, 1957440, 18240, 960, 64,
%e A285616 ...
%t A285616 nn = 6; A[z_] := Sum[2^(2^n - 1) z^n/n!, {n, 0, nn}];
%t A285616 Map[Select[#, # > 0 &] &,Drop[Range[0, nn]! CoefficientList[
%t A285616      Series[(A[z]^u), {z, 0, nn}], {z, u}], 1]] // Grid
%Y A285616 Row sums give A058891.
%Y A285616 Column 1 is A092918.
%K A285616 nonn,tabl
%O A285616 1,1
%A A285616 _Geoffrey Critzer_, Apr 22 2017