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Number of unlabeled sets of subsets covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 sets of subsets.
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%I #5 Aug 13 2019 13:20:37

%S 2,2,4,32,2424

%N Number of unlabeled sets of subsets covering n vertices where every vertex is the unique common element of some subset of the edges, also called unlabeled covering T_1 sets of subsets.

%C Alternatively, these are unlabeled sets of subsets covering n vertices whose dual is a (strict) antichain. The dual of a set of subsets has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. An antichain is a set of subsets where no edge is a subset of any other.

%F a(n) = A326974(n) / 2.

%F a(n > 0) = A326951(n) - A326951(n - 1).

%e Non-isomorphic representatives of the a(0) = 1 through a(2) = 4 sets of subsets:

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

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

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

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

%Y Unlabeled covering sets of subsets are A003181.

%Y The same with T_0 instead of T_1 is A326942.

%Y The non-covering version is A326951 (partial sums).

%Y The labeled version is A326960.

%Y The case without empty edges is A326974.

%Y Cf. A001146, A055621, A059523, A319637, A326961, A326972, A326973, A326976, A326977, A326979.

%K nonn,more

%O 0,1

%A _Gus Wiseman_, Aug 13 2019