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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. 0

%I #10 Apr 22 2017 23:22:49

%S 2,4,4,96,24,8,31840,816,96,16,2147156736,322240,4320,320,32,

%T 9223372011084915712,25767883392,1957440,18240,960,64,

%U 170141183460469231602560095199828453376,129127208335656968192,180389362944,9251200,67200,2688,128

%N 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 E.g.f.: A(x)^y where A(x) = Sum_{n>=0} 2^(2^n-1)x^n/n!.

%e Triangle begins:

%e 2,

%e 4, 4,

%e 96, 24, 8,

%e 31840, 816, 96, 16,

%e 2147156736, 322240, 4320, 320, 32,

%e 9223372011084915712, 25767883392, 1957440, 18240, 960, 64,

%e ...

%t nn = 6; A[z_] := Sum[2^(2^n - 1) z^n/n!, {n, 0, nn}];

%t Map[Select[#, # > 0 &] &,Drop[Range[0, nn]! CoefficientList[

%t Series[(A[z]^u), {z, 0, nn}], {z, u}], 1]] // Grid

%Y Row sums give A058891.

%Y Column 1 is A092918.

%K nonn,tabl

%O 1,1

%A _Geoffrey Critzer_, Apr 22 2017

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)