cp's OEIS Frontend

A322705 Number of k-uniform k-regular hypergraphs spanning n vertices, for some 1 <= k <= n.

%I A322705 #6 Dec 24 2018 07:46:31
%S A322705 1,1,1,2,5,26,472,23342
%N A322705 Number of k-uniform k-regular hypergraphs spanning n vertices, for some 1 <= k <= n.
%C A322705 We define a hypergraph to be any finite set of finite nonempty sets. A hypergraph is k-uniform if all edges contain exactly k vertices, and k-regular if all vertices belong to exactly k edges. The span of a hypergraph is the union of its edges.
%e A322705 The a(3) = 2 hypergraphs:
%e A322705   {{1},{2},{3}}
%e A322705   {{1,2},{1,3},{2,3}}
%e A322705 The a(4) = 5 hypergraphs:
%e A322705   {{1},{2},{3},{4}}
%e A322705   {{1,2},{1,3},{2,4},{3,4}}
%e A322705   {{1,2},{1,4},{2,3},{3,4}}
%e A322705   {{1,3},{1,4},{2,3},{2,4}}
%e A322705   {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
%e A322705 The a(5) = 26 hypergraphs:
%e A322705   {{1},{2},{3},{4},{5}}
%e A322705   {{1,2},{1,3},{2,4},{3,5},{4,5}}
%e A322705   {{1,2},{1,3},{2,5},{3,4},{4,5}}
%e A322705   {{1,2},{1,4},{2,3},{3,5},{4,5}}
%e A322705   {{1,2},{1,4},{2,5},{3,4},{3,5}}
%e A322705   {{1,2},{1,5},{2,3},{3,4},{4,5}}
%e A322705   {{1,2},{1,5},{2,4},{3,4},{3,5}}
%e A322705   {{1,3},{1,4},{2,3},{2,5},{4,5}}
%e A322705   {{1,3},{1,4},{2,4},{2,5},{3,5}}
%e A322705   {{1,3},{1,5},{2,3},{2,4},{4,5}}
%e A322705   {{1,3},{1,5},{2,4},{2,5},{3,4}}
%e A322705   {{1,4},{1,5},{2,3},{2,4},{3,5}}
%e A322705   {{1,4},{1,5},{2,3},{2,5},{3,4}}
%e A322705   {{1,2,3},{1,2,4},{1,3,5},{2,4,5},{3,4,5}}
%e A322705   {{1,2,3},{1,2,4},{1,4,5},{2,3,5},{3,4,5}}
%e A322705   {{1,2,3},{1,2,5},{1,3,4},{2,4,5},{3,4,5}}
%e A322705   {{1,2,3},{1,2,5},{1,4,5},{2,3,4},{3,4,5}}
%e A322705   {{1,2,3},{1,3,4},{1,4,5},{2,3,5},{2,4,5}}
%e A322705   {{1,2,3},{1,3,5},{1,4,5},{2,3,4},{2,4,5}}
%e A322705   {{1,2,4},{1,2,5},{1,3,4},{2,3,5},{3,4,5}}
%e A322705   {{1,2,4},{1,2,5},{1,3,5},{2,3,4},{3,4,5}}
%e A322705   {{1,2,4},{1,3,4},{1,3,5},{2,3,5},{2,4,5}}
%e A322705   {{1,2,4},{1,3,5},{1,4,5},{2,3,4},{2,3,5}}
%e A322705   {{1,2,5},{1,3,4},{1,3,5},{2,3,4},{2,4,5}}
%e A322705   {{1,2,5},{1,3,4},{1,4,5},{2,3,4},{2,3,5}}
%e A322705   {{1,2,3,4},{1,2,3,5},{1,2,4,5},{1,3,4,5},{2,3,4,5}}
%t A322705 Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s,{s,Subsets[Range[n],{k}]}],Sequence@@Table[{x[i],0,k},{i,n}]],{k,1,n}],{n,1,6}]
%Y A322705 Row sums of A322706.
%Y A322705 Cf. A005176, A058891, A059441, A116539, A295193, A299353, A306021, A319056, A319189, A319190, A319612, A321721, A322704.
%K A322705 nonn,more
%O A322705 0,4
%A A322705 _Gus Wiseman_, Dec 23 2018