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%I #14 Jun 14 2013 04:23:33
%S 25,454,3818,21420,92805,335152,1055944,2990020,7767357,18789070,
%T 42797602,92588216,191542842,381000192,731941256,1363109096,
%U 2468549141,4358716470,7520830306,12706161124,21054530855,34269633840,54863015040,86489873580,134406530985
%N Number of 4-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 4 labeled nodes and n hyperedges.
%C T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair of distinct nodes has a hyperedge containing one but not the other node.
%D 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 V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H T. D. Noe, <a href="/A056069/b056069.txt">Table of n, a(n) for n = 4..1000</a>
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>
%F a(n) = C(n + 15, 15) - 12*C(n + 11, 11) + 24*C(n + 9, 9) + 4*C(n + 8, 8) - 18*C(n + 7, 7) + 6*C(n + 6, 6) - 36*C(n + 5, 5) + 36*C(n + 4, 4) + 11*C(n + 3, 3) - 22*C(n + 2, 2) + 6*C(n + 1, 1).
%F Empirical G.f.: x^4*(6*x^10 -62*x^9 +271*x^8 -636*x^7 +800*x^6 -328*x^5 -495*x^4 +812*x^3 -446*x^2 +54*x +25)/(x-1)^16. [_Colin Barker_, May 29 2012]
%Y Cf. A051112 for 4-element (unordered) antichains on a labeled n-element set, A056005.
%K nonn
%O 4,1
%A _Vladeta Jovovic_, Goran Kilibarda, Jul 26 2000