cp's OEIS Frontend

A326951 Number of unlabeled sets of subsets of {1..n} where every covered vertex is the unique common element of some subset of the edges.

%I A326951 #6 Aug 13 2019 13:19:02
%S A326951 2,4,8,40,2464
%N A326951 Number of unlabeled sets of subsets of {1..n} where every covered vertex is the unique common element of some subset of the edges.
%C A326951 Alternatively, these are unlabeled sets of subsets of {1..n} whose dual is a (strict) antichain, also called T_1 sets of subsets. 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. An antichain is a set of subsets where no edge is a subset of any other.
%F A326951 a(n) = 2 * A326972(n).
%F A326951 a(n) = Sum_{k = 0..n} A327011(k).
%e A326951 Non-isomorphic representatives of the a(0) = 2 through a(2) = 8 sets of subsets:
%e A326951   {}    {}        {}
%e A326951   {{}}  {{}}      {{}}
%e A326951         {{1}}     {{1}}
%e A326951         {{},{1}}  {{},{1}}
%e A326951                   {{1},{2}}
%e A326951                   {{},{1},{2}}
%e A326951                   {{1},{2},{1,2}}
%e A326951                   {{},{1},{2},{1,2}}
%Y A326951 Unlabeled sets of subsets are A003180.
%Y A326951 Unlabeled T_0 sets of subsets are A326949.
%Y A326951 The labeled version is A326967.
%Y A326951 The case without empty edges is A326972.
%Y A326951 The covering case is A327011 (first differences).
%Y A326951 Cf. A003181, A059052, A326960, A326965, A326969, A326974, A326976.
%K A326951 nonn,more
%O A326951 0,1
%A A326951 _Gus Wiseman_, Aug 13 2019