

A327229


Number of setsystems covering n vertices with at least one endpoint/leaf.


12




OFFSET

0,3


COMMENTS

Covering means there are no isolated vertices.
A setsystem is a finite set of finite nonempty sets. Elements of a setsystem 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 setsystems with minimum vertexdegree 1.


LINKS

Table of n, a(n) for n=0..4.


FORMULA

Inverse binomial transform of A327228.


EXAMPLE

The a(2) = 4 setsystems:
{{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 noncovering version is A327228.
The specialization to simple graphs is A327227.
The unlabeled version is A327230.
BIInumbers of these setsystems 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,more


AUTHOR

Gus Wiseman, Sep 01 2019


STATUS

approved



