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Number of regular hypergraphs on n labeled vertices with no singletons.
3

%I #4 Dec 24 2018 07:46:22

%S 1,1,2,4,80,209944

%N Number of regular hypergraphs on n labeled vertices with no singletons.

%C 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 The a(3) = 4 edge-sets:

%e {}

%e {{1,2,3}}

%e {{1,2},{1,3},{2,3}}

%e {{1,2},{1,3},{2,3},{1,2,3}}

%t 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 Cf. A058891, A059441, A295193, A306021, A319189, A319190, A319612, A319729, A322698.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Dec 23 2018