A301481 Number of unlabeled uniform hypergraphs spanning n vertices.

1, 1, 2, 4, 12, 58, 2381, 14026281, 29284932065996445, 468863491068204425232922367150021, 1994324729204021501147398087008429476673379600542622915802043462326345

Offset: 0

Author

Gus Wiseman, Jun 19 2018

Keywords

• nonn

Comments

A hypergraph is uniform if all edges have the same size.

Examples

			Non-isomorphic representatives of the a(4) = 12 hypergraphs:
  {{1,2,3,4}}
  {{1,2},{3,4}}
  {{1},{2},{3},{4}}
  {{1,3,4},{2,3,4}}
  {{1,3},{2,4},{3,4}}
  {{1,4},{2,4},{3,4}}
  {{1,2,4},{1,3,4},{2,3,4}}
  {{1,2},{1,3},{2,4},{3,4}}
  {{1,4},{2,3},{2,4},{3,4}}
  {{1,3},{1,4},{2,3},{2,4},{3,4}}
  {{1,2,3},{1,2,4},{1,3,4},{2,3,4}}
  {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..14 (first 13 terms from Andrew Howroyd)

Crossrefs

Row sums of A301922.

Cf. A003465, A038041, A055621, A298422, A301920, A306017-A306021.

Programs

PARI

\\ see A301922 for U(n,k).
a(n)={ if(n==0, 1, sum(k=1, n, U(n,k)-U(n-1,k))) } \\ Andrew Howroyd, Aug 10 2019

Extensions

Terms a(6) and beyond from Andrew Howroyd, Aug 09 2019