A299353 Number of labeled connected uniform hypergraphs spanning n vertices.

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

Offset

0,4

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.

Links

Table of n, a(n) for n=0..10.

Wikipedia, Hypergraph

Example

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}}

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}]

Crossrefs

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

Sequence in context: A354685 A247951 A082100 * A180976 A305844 A303132

Adjacent sequences: A299350 A299351 A299352 * A299354 A299355 A299356

Keyword

nonn

Author

Gus Wiseman, Jun 18 2018

Status

approved