A319190 Number of regular hypergraphs spanning n vertices.

1, 1, 3, 19, 879, 5280907, 1069418570520767

Offset

0,3

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. The span of a hypergraph is the union of its edges.

Links

Table of n, a(n) for n=0..6.

Example

The a(3) = 19 regular hypergraphs:
                 {{1,2,3}}
                {{1},{2,3}}
                {{2},{1,3}}
                {{3},{1,2}}
               {{1},{2},{3}}
            {{1},{2,3},{1,2,3}}
            {{2},{1,3},{1,2,3}}
            {{3},{1,2},{1,2,3}}
            {{1,2},{1,3},{2,3}}
           {{1},{2},{3},{1,2,3}}
           {{1},{2},{1,3},{2,3}}
           {{1},{3},{1,2},{2,3}}
           {{2},{3},{1,2},{1,3}}
        {{1,2},{1,3},{2,3},{1,2,3}}
       {{1},{2},{1,3},{2,3},{1,2,3}}
       {{1},{3},{1,2},{2,3},{1,2,3}}
       {{2},{3},{1,2},{1,3},{1,2,3}}
      {{1},{2},{3},{1,2},{1,3},{2,3}}
  {{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

Mathematica

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}]

Crossrefs

Column sums of A188445.

Cf. A002829, A005176, A049311, A058891, A110100, A110101, A116539, A283877, A295193, A306017, A319189.

Sequence in context: A107706 A330040 A168591 * A350121 A014015 A114301

Adjacent sequences: A319187 A319188 A319189 * A319191 A319192 A319193

Keyword

nonn,more

Author

Gus Wiseman, Dec 17 2018

Extensions

a(6) from Andrew Howroyd, Mar 12 2020

Status

approved