%I
%S 1,1,3,19,879,5280907,1069418570520767
%N Number of regular hypergraphs spanning n vertices.
%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. The span of a hypergraph is the union of its edges.
%e The a(3) = 19 regular hypergraphs:
%e {{1,2,3}}
%e {{1},{2,3}}
%e {{2},{1,3}}
%e {{3},{1,2}}
%e {{1},{2},{3}}
%e {{1},{2,3},{1,2,3}}
%e {{2},{1,3},{1,2,3}}
%e {{3},{1,2},{1,2,3}}
%e {{1,2},{1,3},{2,3}}
%e {{1},{2},{3},{1,2,3}}
%e {{1},{2},{1,3},{2,3}}
%e {{1},{3},{1,2},{2,3}}
%e {{2},{3},{1,2},{1,3}}
%e {{1,2},{1,3},{2,3},{1,2,3}}
%e {{1},{2},{1,3},{2,3},{1,2,3}}
%e {{1},{3},{1,2},{2,3},{1,2,3}}
%e {{2},{3},{1,2},{1,3},{1,2,3}}
%e {{1},{2},{3},{1,2},{1,3},{2,3}}
%e {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
%t Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s,{s,Subsets[Range[n],{1,n}]}],Sequence@@Table[{x[i],0,k},{i,n}]],{k,1,2^n}],{n,5}]
%Y Column sums of A188445.
%Y Cf. A002829, A005176, A049311, A058891, A110100, A110101, A116539, A283877, A295193, A306017, A319189.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Dec 17 2018
%E a(6) from _Andrew Howroyd_, Mar 12 2020
