5,1

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.

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.

K. S. Brown, Dedekind's problem

a(n)=C(n + 127, 127) - 42*C(n + 95, 95) + 210*C(n + 79, 79) + 140*C(n + 71, 71) + 210*C(n + 67, 67) - 84*C(n + 65, 65) + 14*C(n + 64, 64) - 819*C(n + 63, 63) - 2520*C(n + 59, 59) + 2730*C(n + 55, 55) + 840*C(n + 53, 53) + 840*C(n + 51, 51) - 420*C(n + 50, 50) + 2940*C(n + 49, 49) + 630*C(n + 47, 47) - 5040*C(n + 45, 45) + 840*C(n + 44, 44) - 1260*C(n + 43, 43) +

1680*C(n + 42, 42) - 9660*C(n + 41, 41) + 1260*C(n + 40, 40) + 3360*C(n + 39, 39) - 7560*C(n + 38, 38) + 11130*C(n + 37, 37) + 5880*C(n + 36, 36) + 9240*C(n + 35, 35) + 2982*C(n + 34, 34) - 6300*C(n + 33, 33) - 8652*C(n + 32, 32) - 9905*C(n + 31, 31) - 8400*C(n + 30, 30) - 8540*C(n + 29, 29) + 13860*C(n + 28, 28) + 14490*C(n + 27, 27) - 5040*C(n + 26, 26) + 10500*C(n + 25, 25) +

10080*C(n + 24, 24) - 8120*C(n + 23, 23) - 15050*C(n + 22, 22) - 5040*C(n + 21, 21) - 11340*C(n + 20, 20) + 20580*C(n + 19, 19) + 15750*C(n + 18, 18) - 1540*C(n + 17, 17) - 5810*C(n + 16, 16) - 16485*C(n + 15, 15) - 21420*C(n + 14, 14) + 26250*C(n + 13, 13) + 21000*C(n + 12, 12) - 29820*C(n + 11, 11) + 3500*C(n + 10, 10) + 17640*C(n + 9, 9) + 2940*C(n + 8, 8) - 16016*C(n + 7, 7) + 4410*C(n + 6, 6) - 9744*C(n + 5, 5) + 9744*C(n + 4, 4) + 1764*C(n + 3, 3) - 3528*C(n + 2, 2) + 720*C(n + 1, 1).

A051115 for 7-element (unordered) antichains on a labeled n-element set, A056005.

Sequence in context: A103912 A082254 A059050 this_sequence A028519 A107263 A017404

Adjacent sequences: A056070 A056071 A056072 this_sequence A056074 A056075 A056076

nonn

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic (vladeta(AT)eunet.rs), Jul 26 2000