A059584 Triangle T(n,m) of number of labeled m-node T_0-hypergraphs with n hyperedges (empty hyperedges and multiple hyperedges included), m=0,1,...,2^n.

1, 1, 1, 2, 2, 1, 3, 7, 12, 12, 1, 4, 16, 68, 292, 1120, 3360, 6720, 6720, 1, 5, 30, 235, 2251, 23520, 245280, 2412480, 21631680, 172972800, 1210809600, 7264857600, 36324288000, 145297152000, 435891456000, 871782912000, 871782912000

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Jan 23 2001

Keywords

• easy
• nonn
• tabf

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

			Triangle starts:
1, 1;
1, 2, 2;
1, 3, 7, 12, 12;
1, 4, 16, 68, 292, 1120, 3360, 6720, 6720;
...
There are 7 2-node T_0-hypergraphs with 2 hyperedges: {{}, {1}}, {{}, {2}}, {{1}, {1}}, {{1}, {2}}, {{1}, {1, 2}}, {{2}, {2}} and {{2}, {1, 2}}.
		

Crossrefs

Cf. A059084, A051362 (=T(n,2)), A059585 (=T(n,3)), A059586 (row sums).

Formula

T(n,m) = Sum_{i=0..m} stirling1(m, i)*binomial(2^i+n-1, n).