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%I A319767 #5 Sep 28 2018 15:22:52
%S A319767 1,1,1,5,73
%N A319767 Number of non-isomorphic intersecting set systems spanning n vertices whose dual is also an intersecting set system.
%C A319767 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}}.
%C A319767 A multiset partition is intersecting iff no two parts are disjoint. The dual of a multiset partition is intersecting iff every pair of distinct vertices appear together in some part.
%C A319767 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 A319767 Non-isomorphic representatives of the a(1) = 1 through a(3) = 5 multiset partitions:
%e A319767 1: {{1}}
%e A319767 2: {{2},{1,2}}
%e A319767 3: {{3},{2,3},{1,2,3}}
%e A319767 {{1,2},{1,3},{2,3}}
%e A319767 {{1,3},{2,3},{1,2,3}}
%e A319767 {{3},{1,3},{2,3},{1,2,3}}
%e A319767 {{1,2},{1,3},{2,3},{1,2,3}}
%Y A319767 Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.
%Y A319767 Cf. A319752, A319765, A319766, A319768, A319769, A319773, A319774.
%K A319767 nonn,more
%O A319767 0,4
%A A319767 _Gus Wiseman_, Sep 27 2018