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 A327228 Number of set-systems with n vertices and at least one endpoint/leaf. 8
 0, 1, 6, 65, 3297 (list; graph; refs; listen; history; text; internal format)
 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. 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. Cf. A059167, A327098, A327103, A327104, A327107, A327197, A327227, A327230. Sequence in context: A121017 A239998 A278841 * A284067 A137121 A110222 Adjacent sequences:  A327225 A327226 A327227 * A327229 A327230 A327231 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 01 2019 STATUS approved

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Last modified February 23 07:11 EST 2020. Contains 332159 sequences. (Running on oeis4.)