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A327228
Number of set-systems with n vertices and at least one endpoint/leaf.
9
0, 1, 6, 65, 3297, 2537672, 412184904221, 4132070624893905681577, 174224571863520492218909428465944685216436, 133392486801388257127953774730008469745829658368044283629394202488602260177922751
OFFSET
0,3
COMMENTS
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 set-systems with minimum covered vertex-degree 1.
LINKS
FORMULA
Binomial transform of A327229.
a(n) = A058891(n+1) - A330059(n). - Andrew Howroyd, Jan 21 2023
EXAMPLE
The a(2) = 6 set-systems:
{{1}}
{{2}}
{{1,2}}
{{1},{2}}
{{1},{1,2}}
{{2},{1,2}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 4}]
CROSSREFS
The covering version is A327229.
The specialization to simple graphs is A245797.
BII-numbers of these set-systems are A327105.
Sequence in context: A121017 A239998 A278841 * A359854 A284067 A137121
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 01 2019
EXTENSIONS
Terms a(5) and beyond from Andrew Howroyd, Jan 21 2023
STATUS
approved