

A059051


Number of ordered T_0antichains on an unlabeled nset; labeled T_1hypergraphs with n (not necessary empty) distinct hyperedges.


2




OFFSET

0,1


COMMENTS

An antichain on a set is a T_0antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point. T_1hypergraph is a hypergraph which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v.


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, 127138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.


LINKS

Table of n, a(n) for n=0..5.


FORMULA

a(n)=Sum_{m=0..C(n, floor(n/2))} A(m, n), where A(m, n) is number of melement ordered T_0antichains on an unlabeled nset. Cf. A059048.


EXAMPLE

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. a(n) = column sums of A059048.


CROSSREFS

Cf. A059048A059050, A059052.
Sequence in context: A236406 A202714 A022662 * A130069 A120007 A092509
Adjacent sequences: A059048 A059049 A059050 * A059052 A059053 A059054


KEYWORD

hard,more,nonn


AUTHOR

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000


STATUS

approved



