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

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 01 2019

EXTENSIONS

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

STATUS

approved