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%I #4 Sep 02 2019 08:05:45
%S 0,1,4,18,216
%N Number of non-isomorphic set-systems with n vertices and at least one endpoint/leaf.
%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 covered vertex-degree 1.
%e Non-isomorphic representatives of the a(1) = 1 through a(3) = 18 set-systems:
%e {{1}} {{1}} {{1}}
%e {{1,2}} {{1,2}}
%e {{1},{2}} {{1},{2}}
%e {{1},{1,2}} {{1,2,3}}
%e {{1},{1,2}}
%e {{1},{2,3}}
%e {{1},{1,2,3}}
%e {{1,2},{1,3}}
%e {{1},{2},{3}}
%e {{1,2},{1,2,3}}
%e {{1},{2},{1,3}}
%e {{1},{1,2},{1,3}}
%e {{1},{1,2},{2,3}}
%e {{1},{2},{1,2,3}}
%e {{1},{1,2},{1,2,3}}
%e {{1},{2},{3},{1,2}}
%e {{1},{2},{1,2},{1,3}}
%e {{1},{2},{1,2},{1,2,3}}
%Y Unlabeled set-systems are A000612.
%Y The labeled version is A327228.
%Y The covering version is A327230 (first differences).
%Y Cf. A002494, A245797, A261919, A283877, A327103, A327105, A327197, A327227, A327229, A327336.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Sep 02 2019
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