A327229 Number of set-systems covering n vertices with at least one endpoint/leaf.

0, 1, 4, 50, 3069, 2521782, 412169726428, 4132070622008664529903, 174224571863520492185852863478334475199686, 133392486801388257127953774730008469744261637221272599199572772174870315402893538

Offset

0,3

Comments

Covering means there are no isolated vertices.

A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. A leaf is an edge containing a vertex that does not belong to any other edge, while an endpoint is a vertex belonging to only one edge.

Also covering set-systems with minimum vertex-degree 1.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..12

Formula

Inverse binomial transform of A327228.

Example

The a(2) = 4 set-systems:
  {{1,2}}
  {{1},{2}}
  {{1},{1,2}}
  {{2},{1,2}}

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Union@@#==Range[n]&&Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 3}]

Crossrefs

The non-covering version is A327228.

The specialization to simple graphs is A327227.

The unlabeled version is A327230.

BII-numbers of these set-systems are A327105.

Cf. A003465, A245797, A327079, A327098, A327103, A327107, A327197.

Sequence in context: A201209 A026865 A016078 * A231832 A193157 A235604

Adjacent sequences: A327226 A327227 A327228 * A327230 A327231 A327232

Keyword

nonn

Author

Gus Wiseman, Sep 01 2019

Extensions

Terms a(5) and beyond from Andrew Howroyd, Jan 21 2023

Status

approved