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%I A322704 #4 Dec 24 2018 07:46:22
%S A322704 1,1,2,4,80,209944
%N A322704 Number of regular hypergraphs on n labeled vertices with no singletons.
%C A322704 We define a hypergraph to be any finite set of finite nonempty sets. A hypergraph is regular if all vertices have the same degree.
%e A322704 The a(3) = 4 edge-sets:
%e A322704   {}
%e A322704   {{1,2,3}}
%e A322704   {{1,2},{1,3},{2,3}}
%e A322704   {{1,2},{1,3},{2,3},{1,2,3}}
%t A322704 Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s,{s,Subsets[Range[n],{2,n}]}],Sequence@@Table[{x[i],0,k},{i,n}]],{k,0,2^n-n-1}],{n,1,5}]
%Y A322704 Cf. A058891, A059441, A295193, A306021, A319189, A319190, A319612, A319729, A322698.
%K A322704 nonn,more
%O A322704 0,3
%A A322704 _Gus Wiseman_, Dec 23 2018

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