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A059052
Number of n-element unlabeled ordered T_0-antichains; T_1-hypergraphs (with empty hyperedge but without multiple hyperedges) on n labeled nodes.
22
2, 4, 4, 72, 38040, 4020463392, 18438434825136728352, 340282363593610211921722192165556850240, 115792089237316195072053288318104625954343609704705784618785209431974668731584
OFFSET
0,1
COMMENTS
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.
REFERENCES
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
LINKS
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, in Russian, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, English translation, in Discrete Mathematics and Applications, 9, (1999), no. 6.
FORMULA
a(n) = Sum_{m=0..2^n} A(n, m), where A(n, m) is number of n-element ordered T_0-antichains on an unlabeled m-set. Cf. A059048.
a(n) = row sums of A059048.
EXAMPLE
a(3) = 2 + 13 + 26 + 22 + 8 + 1. a(6) = 2^64 - 30*2^48 + 120*2^40 + 60*2^36 + 60*2^34 - 12*2^33 - 345*2^32 - 720*2^30 + 810*2^28 + 120*2^27 + 480*2^26 + 360*2^25 - 480*2^24 - 720*2^23 - 240*2^22 - 540*2^21 + 1380*2^20 + 750*2^19 + 60*2^18 - 210*2^17 - 1535*2^16 - 1820*2^15 + 2250*2^14 + 1800*2^13 - 2820*2^12 + 300*2^11 + 2040*2^10 + 340*2^9 - 1815*2^8 + 510*2^7 - 1350*2^6 + 1350*2^5 + 274*2^4 - 548*2^3 + 120*2^2.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Dec 19 2000
STATUS
approved