# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a327228 Showing 1-1 of 1 %I A327228 #8 Jan 21 2023 16:12:01 %S A327228 0,1,6,65,3297,2537672,412184904221,4132070624893905681577, %T A327228 174224571863520492218909428465944685216436, %U A327228 133392486801388257127953774730008469745829658368044283629394202488602260177922751 %N A327228 Number of set-systems with n vertices and at least one endpoint/leaf. %C A327228 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. %C A327228 Also set-systems with minimum covered vertex-degree 1. %H A327228 Andrew Howroyd, Table of n, a(n) for n = 0..12 %F A327228 Binomial transform of A327229. %F A327228 a(n) = A058891(n+1) - A330059(n). - _Andrew Howroyd_, Jan 21 2023 %e A327228 The a(2) = 6 set-systems: %e A327228 {{1}} %e A327228 {{2}} %e A327228 {{1,2}} %e A327228 {{1},{2}} %e A327228 {{1},{1,2}} %e A327228 {{2},{1,2}} %t A327228 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Min@@Length/@Split[Sort[Join@@#]]==1&]],{n,0,4}] %Y A327228 The covering version is A327229. %Y A327228 The specialization to simple graphs is A245797. %Y A327228 BII-numbers of these set-systems are A327105. %Y A327228 Cf. A058891, A059167, A327098, A327103, A327104, A327107, A327197, A327227, A327230, A330059. %K A327228 nonn %O A327228 0,3 %A A327228 _Gus Wiseman_, Sep 01 2019 %E A327228 Terms a(5) and beyond from _Andrew Howroyd_, Jan 21 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE