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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.

%I A059584 #14 Apr 28 2016 11:26:49
%S A059584 1,1,1,2,2,1,3,7,12,12,1,4,16,68,292,1120,3360,6720,6720,1,5,30,235,
%T A059584 2251,23520,245280,2412480,21631680,172972800,1210809600,7264857600,
%U A059584 36324288000,145297152000,435891456000,871782912000,871782912000
%N 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.
%C A059584 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 A059584 T(n,m) = Sum_{i=0..m} stirling1(m, i)*binomial(2^i+n-1, n).
%e A059584 Triangle starts:
%e A059584 1, 1;
%e A059584 1, 2, 2;
%e A059584 1, 3, 7, 12, 12;
%e A059584 1, 4, 16, 68, 292, 1120, 3360, 6720, 6720;
%e A059584 ...
%e A059584 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 A059584 Cf. A059084, A051362 (=T(n,2)), A059585 (=T(n,3)), A059586 (row sums).
%K A059584 easy,nonn,tabf
%O A059584 0,4
%A A059584 _Vladeta Jovovic_, Goran Kilibarda, Jan 23 2001