A322704 Number of regular hypergraphs on n labeled vertices with no singletons.

1, 1, 2, 4, 80, 209944

Offset: 0

Author

Gus Wiseman, Dec 23 2018

Keywords

• nonn
• more

Comments

We define a hypergraph to be any finite set of finite nonempty sets. A hypergraph is regular if all vertices have the same degree.

Examples

			The a(3) = 4 edge-sets:
  {}
  {{1,2,3}}
  {{1,2},{1,3},{2,3}}
  {{1,2},{1,3},{2,3},{1,2,3}}
		

Crossrefs

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

Programs

Mathematica

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}]