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A319190 Number of regular hypergraphs spanning n vertices. 17
1, 1, 3, 19, 879, 5280907 (list; graph; refs; listen; history; text; internal format)
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..5.

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

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

Sequence in context: A272571 A107706 A168591 * A014015 A114301 A258669

Adjacent sequences:  A319187 A319188 A319189 * A319191 A319192 A319193

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Dec 17 2018

STATUS

approved

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)