|
%I #7 Apr 07 2018 03:55:35
%S 1,1,0,1,5,388,477965,19199206747,48058624241034238,
%T 14791854612528152343049939,112039538006858119010793653395340973,
%U 42077073837090084518028123082446810913910363417140
%N Number of families of 3-subsets of an n-set that cover all 2-subsets.
%C Number of 3-uniform simple hypergraphs on n vertices such that each pair of vertices are together in some edge.
%F a(n) = SUM (-1)^e(G) (n!/a(G)) 2^t(G), where the sum is over the unlabeled graphs G with n vertices, e(G) is the number of edges in the complement of G, a(G) is the order of the automorphism group of G, and t(G) is the number of triangles in G.
%e For n=4 the a(4)=5 solutions are {123,124,134}, {123,124,234},{123,134,234},{124,134,234}, {123,124,134,234}
%K nonn,hard
%O 0,5
%A _Brendan McKay_, Apr 07 2018
|
