login
A327229
Number of set-systems covering n vertices with at least one endpoint/leaf.
13
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
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.
Sequence in context: A201209 A026865 A016078 * A231832 A193157 A235604
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 01 2019
EXTENSIONS
Terms a(5) and beyond from Andrew Howroyd, Jan 21 2023
STATUS
approved