cp's OEIS Frontend

A327229 Number of set-systems covering n vertices with at least one endpoint/leaf.

%I A327229 #8 Jan 21 2023 16:11:57
%S A327229 0,1,4,50,3069,2521782,412169726428,4132070622008664529903,
%T A327229 174224571863520492185852863478334475199686,
%U A327229 133392486801388257127953774730008469744261637221272599199572772174870315402893538
%N A327229 Number of set-systems covering n vertices with at least one endpoint/leaf.
%C A327229 Covering means there are no isolated vertices.
%C A327229 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 A327229 Also covering set-systems with minimum vertex-degree 1.
%H A327229 Andrew Howroyd, <a href="/A327229/b327229.txt">Table of n, a(n) for n = 0..12</a>
%F A327229 Inverse binomial transform of A327228.
%e A327229 The a(2) = 4 set-systems:
%e A327229   {{1,2}}
%e A327229   {{1},{2}}
%e A327229   {{1},{1,2}}
%e A327229   {{2},{1,2}}
%t A327229 Table[Length[Select[Subsets[Subsets[Range[n],{1,n}]],Union@@#==Range[n]&&Min@@Length/@Split[Sort[Join@@#]]==1&]],{n,0,3}]
%Y A327229 The non-covering version is A327228.
%Y A327229 The specialization to simple graphs is A327227.
%Y A327229 The unlabeled version is A327230.
%Y A327229 BII-numbers of these set-systems are A327105.
%Y A327229 Cf. A003465, A245797, A327079, A327098, A327103, A327107, A327197.
%K A327229 nonn
%O A327229 0,3
%A A327229 _Gus Wiseman_, Sep 01 2019
%E A327229 Terms a(5) and beyond from _Andrew Howroyd_, Jan 21 2023