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Number of antichains of nonempty subsets of {1..n} that are either non-connected or non-covering (spanning edge-connectivity 0).
8

%I #4 Sep 11 2019 20:22:08

%S 1,1,4,14,83,1232,84625,109147467,38634257989625

%N Number of antichains of nonempty subsets of {1..n} that are either non-connected or non-covering (spanning edge-connectivity 0).

%C An antichain is a set of sets, none of which is a subset of any other. It is covering if there are no isolated vertices.

%C The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.

%F a(n) = A120338(n) + A014466(n) - A006126(n).

%e The a(1) = 1 through a(3) = 14 antichains:

%e {} {} {}

%e {{1}} {{1}}

%e {{2}} {{2}}

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

%e {{1,2}}

%e {{1,3}}

%e {{2,3}}

%e {{1},{2}}

%e {{1},{3}}

%e {{2},{3}}

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

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

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

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

%Y Column k = 0 of A327352.

%Y The covering case is A120338.

%Y The unlabeled version is A327437.

%Y The non-spanning edge-connectivity version is A327354.

%Y Cf. A014466, A327071, A327148, A327353, A327426.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Sep 10 2019