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 A327229 Number of set-systems covering n vertices with at least one endpoint/leaf. 12
 0, 1, 4, 50, 3069 (list; graph; refs; listen; history; text; internal format)
 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. 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

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)