%I #5 Sep 02 2019 08:05:05

%S 0,1,3,14,198

%N Number of non-isomorphic set-systems covering n vertices with 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 vertex-degree 1.

%e Non-isomorphic representatives of the a(1) = 1 through a(3) = 14 set-systems:

%e {{1}} {{1,2}} {{1,2,3}}

%e {{1},{2}} {{1},{2,3}}

%e {{2},{1,2}} {{1},{2},{3}}

%e {{1,3},{2,3}}

%e {{3},{1,2,3}}

%e {{1},{3},{2,3}}

%e {{2,3},{1,2,3}}

%e {{2},{1,3},{2,3}}

%e {{2},{3},{1,2,3}}

%e {{3},{1,3},{2,3}}

%e {{1},{2},{3},{2,3}}

%e {{3},{2,3},{1,2,3}}

%e {{2},{3},{1,3},{2,3}}

%e {{2},{3},{2,3},{1,2,3}}

%Y Unlabeled covering set-systems are A055621.

%Y The labeled version is A327229.

%Y The non-covering version is A327335 (partial sums).

%Y Cf. A002494, A245797, A261919, A283877, A327103, A327105, A327197, A327227, A327228.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 01 2019