%I #7 May 10 2013 12:44:29
%S 4,20,65,170,383,779,1470,2611,4418,7182,11283,17213,25601,37230,
%T 53074,74327,102434,139133,186501,246988,323479,419344,538492,685438,
%U 865376,1084236,1348777,1666664,2046551,2498179,3032482,3661673,4399374
%N Number of asymmetric types of (3,n)-hypergraphs without isolated nodes, under action of symmetric group S_3; asymmetric n-covers of an unlabeled 3-set.
%C Cover may include both empty sets and multiple occurrences of a subset.
%F G.f. : (1/(1-x)^8-3/(1-x)^4/(1-x^2)^2+2/(1-x)^2/(1-x^3)^2-3/(1-x)^4+3/(1-x)^2/(1-x^2)+6/(1-x)^2-6/(1-x))/6.
%e There are 4 asymmetric (3,3)-hypergraphs without isolated nodes: {{1,2},{1,2},{1,3}}, {{1},{1,2},{1,2,3}}, {{1},{1,2},{2,3}}, {{1},{2},{1,3}}.
%Y Cf. A005745.
%K nonn
%O 3,1
%A _Vladeta Jovovic_, Jul 09 2000
%E More terms from _James A. Sellers_, Jul 11 2000