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A056164 Number of ordered antichain covers of an unlabeled n-set; labeled T_1-hypergraphs (without empty hyperedges) with n hyperedges. 0
1, 2, 6, 109, 191177 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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.
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.
LINKS
K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers
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.
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.
CROSSREFS
Sequence in context: A059088 A216151 A057771 * A156500 A264889 A365669
KEYWORD
hard,more,nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jul 31 2000
STATUS
approved

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