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A056164
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Number of ordered antichain covers of an unlabeled n-set; labeled T_1-hypergraphs (without empty hyperedges) with n hyperedges.
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0
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OFFSET
| 1,2
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COMMENTS
| A 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.
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REFERENCES
| 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)
V. Jovovic and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
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LINKS
| K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers"
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FORMULA
| a(n)=Sum_{k=1..C(n, floor(n/2))}b(k, n) where b(k, n) is the number of k-element ordered antichains covers of an unlabeled n-set.
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EXAMPLE
| There are 6 ordered antichain covers on an unlabeled 3-set: ({1,2,3}), ({1},{2,3}), ({2,3},{1}), ({1,2},{1,3}), ({1},{2},{3}), ({1,2},{1,3},{2,3}).
a(3)=1+3+2=6; a(4)=1+6+17+25+30+30=109; a(5)=1+10+71+429+2176+8310+20580+38640+60480+60480=191177.
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CROSSREFS
| Cf. A056074, A056090, A056093, A000372, A056005, A056069-A056071, A056073, A056046-A056049, A056052, A056101, A056104, A051112-A051118.
Sequence in context: A181036 A059088 A057771 * A156500 A075391 A058251
Adjacent sequences: A056161 A056162 A056163 * A056165 A056166 A056167
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KEYWORD
| hard,more,nonn
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AUTHOR
| Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jul 31 2000
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