A059584 - OEIS

%I #14 Apr 28 2016 11:26:49

%S 1,1,1,2,2,1,3,7,12,12,1,4,16,68,292,1120,3360,6720,6720,1,5,30,235,

%T 2251,23520,245280,2412480,21631680,172972800,1210809600,7264857600,

%U 36324288000,145297152000,435891456000,871782912000,871782912000

%N 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.

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

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

%e Triangle starts:

%e 1, 1;

%e 1, 2, 2;

%e 1, 3, 7, 12, 12;

%e 1, 4, 16, 68, 292, 1120, 3360, 6720, 6720;

%e ...

%e 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}}.

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

%K easy,nonn,tabf

%O 0,4

%A _Vladeta Jovovic_, Goran Kilibarda, Jan 23 2001