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.

2, 4, 4, 96, 24, 8, 31840, 816, 96, 16, 2147156736, 322240, 4320, 320, 32, 9223372011084915712, 25767883392, 1957440, 18240, 960, 64, 170141183460469231602560095199828453376, 129127208335656968192, 180389362944, 9251200, 67200, 2688, 128

Offset: 1

Author

Geoffrey Critzer, Apr 22 2017

Keywords

• nonn
• tabl

Examples

			Triangle begins:
2,
4, 4,
96, 24, 8,
31840, 816, 96, 16,
2147156736, 322240, 4320, 320, 32,
9223372011084915712, 25767883392, 1957440, 18240, 960, 64,
...
		

Crossrefs

Row sums give A058891.

Column 1 is A092918.

Programs

Mathematica

nn = 6; A[z_] := Sum[2^(2^n - 1) z^n/n!, {n, 0, nn}];
Map[Select[#, # > 0 &] &,Drop[Range[0, nn]! CoefficientList[
     Series[(A[z]^u), {z, 0, nn}], {z, u}], 1]] // Grid

Formula

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