A299353 Number of labeled connected uniform hypergraphs spanning n vertices.

1, 1, 1, 5, 50, 1713, 1101990, 68715891672, 1180735735356264714926, 170141183460507906731293351306487161569, 7237005577335553223087828975127304177495735363998991435497132228228565768846

Offset: 0

Author

Gus Wiseman, Jun 18 2018

Keywords

• nonn

Comments

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

Let T be the regular triangle A299354, where column k is the logarithmic transform of the inverse binomial transform of c(d) = 2^binomial(d,k). Then a(n) is the sum of row n.

Examples

			The a(3) = 5 hypergraphs:
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,3},{2,3}}
		

Links

• Wikipedia, Hypergraph

Crossrefs

Cf. A000005, A001315, A006126, A006129, A038041, A048143, A298422, A299354, A299471, A306020, A306021.

Programs

Mathematica

nn=10;Table[Sum[SeriesCoefficient[Log[Sum[x^m/m!*(-1)^(m-d)*Binomial[m,d]*2^Binomial[d,k],{m,0,n},{d,0,m}]],{x,0,n}]*n!,{k,n}],{n,nn}]