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%I #13 Jan 29 2023 19:19:03
%S 2,3,2,4,99,190866
%N Number of ordered T_0-antichains on an unlabeled n-set; labeled T_1-hypergraphs with n (not necessarily empty) distinct hyperedges.
%C An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point. T_1-hypergraph is a hypergraph which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v.
%D V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.4213/dm398">On the number of Boolean functions in the Post classes F^{mu}_8</a>, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
%H V. Jovovic, G. Kilibarda, <a href="http://dx.doi.org/10.1515/dma.1999.9.6.593">On the number of Boolean functions in the Post classes F^{mu}_8</a>, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.
%F a(n) = Sum_{m=0..C(n, floor(n/2))} A(m, n), where A(m, n) is number of m-element ordered T_0-antichains on an unlabeled n-set. Cf. A059048.
%F a(n) = column sums of A059048.
%e a(0) = 1 + 1, a(1) = 1 + 2, a(2) = 1 + 1, a(3) = 2 + 2, a(4) = 1 + 13 + 25 + 30 + 30, a(5) = 26 + 354 + 2086 + 8220 + 20580 + 38640 + 60480 + 60480.
%Y Cf. A059048-A059050, A059052.
%K hard,more,nonn
%O 0,1
%A _Vladeta Jovovic_, Goran Kilibarda, Dec 19 2000