A059586 Number of labeled T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included).

2, 5, 35, 18301, 2369751675482, 5960531437867327674550533616796025, 479047836152505670895481842190009123676957243077039723706127824160370689849840668444493

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Jan 23 2001

Keywords

• easy
• nonn

Comments

A hypergraph is a T_0 hypergraph if for every two distinct nodes there exists a hyperedge containing one but not the other node.

Examples

			a(3) = (1/3!) * (2 * [2! * e] + 3 * [4! * e] + [8! * e]) = (1/3!) * (2 * 5 + 3 * 65 + 109601) = 18301, where [k! * e] := floor(k! * exp(1)).
		

Crossrefs

Cf. A000522, A059086, A059584, A059585.

Programs

Maple

with(combinat): Digits := 1000: f := n->(1/n!)*sum(abs(stirling1(n,i))*floor((2^i)!*exp(1)), i=0..n): for n from 0 to 8 do printf(`%d,`,f(n)) od:

Formula

a(n)=(1/n!)*Sum_{k=0..n} |stirling1(n, k)|*floor((2^k)!*exp(1)).

Extensions

More terms from James Sellers, Jan 24 2001