cp's OEIS Frontend

A319766 Number of non-isomorphic strict intersecting multiset partitions (sets of multisets) of weight n whose dual is also a strict intersecting multiset partition.

%I A319766 #6 Sep 28 2018 15:22:45
%S A319766 1,1,1,4,6,14,31,64,145,324,753
%N A319766 Number of non-isomorphic strict intersecting multiset partitions (sets of multisets) of weight n whose dual is also a strict intersecting multiset partition.
%C A319766 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 A319766 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 A319766 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 A319766 Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset partitions:
%e A319766 1: {{1}}
%e A319766 2: {{1,1}}
%e A319766 3: {{1,1,1}}
%e A319766    {{1,2,2}}
%e A319766    {{1},{1,1}}
%e A319766    {{2},{1,2}}
%e A319766 4: {{1,1,1,1}}
%e A319766    {{1,2,2,2}}
%e A319766    {{1},{1,1,1}}
%e A319766    {{1},{1,2,2}}
%e A319766    {{2},{1,2,2}}
%e A319766    {{1,2},{2,2}}
%e A319766 5: {{1,1,1,1,1}}
%e A319766    {{1,1,2,2,2}}
%e A319766    {{1,2,2,2,2}}
%e A319766    {{1},{1,1,1,1}}
%e A319766    {{1},{1,2,2,2}}
%e A319766    {{2},{1,1,2,2}}
%e A319766    {{2},{1,2,2,2}}
%e A319766    {{2},{1,2,3,3}}
%e A319766    {{1,1},{1,1,1}}
%e A319766    {{1,1},{1,2,2}}
%e A319766    {{1,2},{1,2,2}}
%e A319766    {{1,2},{2,2,2}}
%e A319766    {{2,2},{1,2,2}}
%e A319766    {{2},{1,2},{2,2}}
%Y A319766 Cf. A007716, A281116, A283877, A305854, A306006,  A316980, A316983, A317757, A319616.
%Y A319766 Cf. A319752, A319765, A319767, A319768, A319769, A319773, A319774.
%K A319766 nonn,more
%O A319766 0,4
%A A319766 _Gus Wiseman_, Sep 27 2018