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%I #5 Sep 28 2018 15:23:49
%S 1,0,1,1,2,5,13,28,72,181,483
%N Number of non-isomorphic set systems of weight n with empty intersection whose dual is also a set system with empty intersection.
%C The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. The dual of a multiset partition has empty intersection iff no part contains all the vertices.
%C The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%e Non-isomorphic representatives of the a(2) = 1 through a(6) = 13 multiset partitions:
%e 2: {{1},{2}}
%e 3: {{1},{2},{3}}
%e 4: {{1},{3},{2,3}}
%e {{1},{2},{3},{4}}
%e 5: {{1},{2,4},{3,4}}
%e {{2},{1,3},{2,3}}
%e {{1},{2},{3},{2,3}}
%e {{1},{2},{4},{3,4}}
%e {{1},{2},{3},{4},{5}}
%e 6: {{3},{1,4},{2,3,4}}
%e {{1,2},{1,3},{2,3}}
%e {{1,3},{2,4},{3,4}}
%e {{1},{2},{1,3},{2,3}}
%e {{1},{2},{3,5},{4,5}}
%e {{1},{3},{4},{2,3,4}}
%e {{1},{3},{2,4},{3,4}}
%e {{1},{4},{2,4},{3,4}}
%e {{2},{3},{1,3},{2,3}}
%e {{2},{4},{1,2},{3,4}}
%e {{1},{2},{3},{4},{3,4}}
%e {{1},{2},{3},{5},{4,5}}
%e {{1},{2},{3},{4},{5},{6}}
%Y Cf. A007716, A049311, A281116, A283877, A316980, A317752, A317755, A317757.
%Y Cf. A319775, A319779, A319781, A319783.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Sep 27 2018
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