cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327228 Number of set-systems with n vertices and at least one endpoint/leaf.

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%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, <a href="/A327228/b327228.txt">Table of n, a(n) for n = 0..12</a>
%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