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A319190 Number of regular hypergraphs spanning n vertices. 20

%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

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Last modified December 2 14:54 EST 2020. Contains 338877 sequences. (Running on oeis4.)