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%I #6 Aug 13 2019 13:19:02
%S 2,4,8,40,2464
%N 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 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 a(n) = 2 * A326972(n).
%F a(n) = Sum_{k = 0..n} A327011(k).
%e Non-isomorphic representatives of the a(0) = 2 through a(2) = 8 sets of subsets:
%e {} {} {}
%e {{}} {{}} {{}}
%e {{1}} {{1}}
%e {{},{1}} {{},{1}}
%e {{1},{2}}
%e {{},{1},{2}}
%e {{1},{2},{1,2}}
%e {{},{1},{2},{1,2}}
%Y Unlabeled sets of subsets are A003180.
%Y Unlabeled T_0 sets of subsets are A326949.
%Y The labeled version is A326967.
%Y The case without empty edges is A326972.
%Y The covering case is A327011 (first differences).
%Y Cf. A003181, A059052, A326960, A326965, A326969, A326974, A326976.
%K nonn,more
%O 0,1
%A _Gus Wiseman_, Aug 13 2019
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