%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