A322704 Number of regular hypergraphs on n labeled vertices with no singletons.

1, 1, 2, 4, 80, 209944

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.

Links

Table of n, a(n) for n=0..5.

Example

The a(3) = 4 edge-sets:
  {}
  {{1,2,3}}
  {{1,2},{1,3},{2,3}}
  {{1,2},{1,3},{2,3},{1,2,3}}

Mathematica

Table[Sum[SeriesCoefficient[Product[1+Times@@x/@s, {s, Subsets[Range[n], {2, n}]}], Sequence@@Table[{x[i], 0, k}, {i, n}]], {k, 0, 2^n-n-1}], {n, 1, 5}]

Crossrefs

Cf. A058891, A059441, A295193, A306021, A319189, A319190, A319612, A319729, A322698.

Sequence in context: A334336 A092932 A102663 * A076961 A012439 A012435

Adjacent sequences: A322701 A322702 A322703 * A322705 A322706 A322707

Keyword

nonn,more

Author

Gus Wiseman, Dec 23 2018

Status

approved