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A059049 Number of 6-element ordered T_0-antichains on an unlabeled n-set; T_1-hypergraphs on 6 labeled nodes with n (not necessarily empty) distinct hyperedges (n=0,1,...,64).

%I A059049 #13 Jan 29 2023 19:32:19
%S A059049 0,0,0,0,30,8220,738842,25256626,464670831,5570534392,48655319306,
%T A059049 332222541564,1859009659336,8811850222304,36244568422086,
%U A059049 131710639199900,428697293437675,1263065928235140,3396450715952370
%N A059049 Number of 6-element ordered T_0-antichains on an unlabeled n-set; T_1-hypergraphs on 6 labeled nodes with n (not necessarily empty) distinct hyperedges (n=0,1,...,64).
%C A059049 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 A059049 V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
%D A059049 V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H A059049 Sean A. Irvine, <a href="/A059049/b059049.txt">Table of n, a(n) for n = 0..64</a>
%F A059049 a(n)=C(64, n) - 30*C(48, n) + 120*C(40, n) + 60*C(36, n) + 60*C(34, n) - 12*C(33, n) - 345*C(32, n) - 720*C(30, n) + 810*C(28, n) + 120*C(27, n) + 480*C(26, n) + 360*C(25, n) - 480*C(24, n) - 720*C(23, n) - 240*C(22, n) - 540*C(21, n) + 1380*C(20, n) + 750*C(19, n) + 60*C(18, n) - 210*C(17, n) - 1535*C(16, n) - 1820*C(15, n) + 2250*C(14, n) + 1800*C(13, n) - 2820*C(12, n) + 300*C(11, n) + 2040*C(10, n) + 340*C(9, n) - 1815*C(8, n) + 510*C(7, n) - 1350*C(6, n) + 1350*C(5, n) + 274*C(4, n) - 548*C(3, n) + 120*C(2, n).
%Y A059049 Cf. A059048, A059050-A059052.
%K A059049 fini,full,nonn
%O A059049 0,5
%A A059049 _Vladeta Jovovic_, Goran Kilibarda, Dec 19 2000