A319190 - OEIS

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A319190

Number of regular hypergraphs spanning n vertices.

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

(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..6.

EXAMPLE

The a(3) = 19 regular hypergraphs:

{{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: A373626 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