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