cp's OEIS Frontend

A319768 Number of non-isomorphic strict multiset partitions (sets of multisets) of weight n whose dual is a (not necessarily strict) intersecting multiset partition.

%I A319768 #5 Sep 28 2018 15:23:02
%S A319768 1,1,2,5,11,25,63,144,364,905,2356
%N A319768 Number of non-isomorphic strict multiset partitions (sets of multisets) of weight n whose dual is a (not necessarily strict) intersecting multiset partition.
%C A319768 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 A319768 The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
%C A319768 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.
%e A319768 Non-isomorphic representatives of the a(1) = 1 through a(4) = 11 multiset partitions:
%e A319768 1: {{1}}
%e A319768 2: {{1,1}}
%e A319768    {{1,2}}
%e A319768 3: {{1,1,1}}
%e A319768    {{1,2,2}}
%e A319768    {{1,2,3}}
%e A319768    {{1},{1,1}}
%e A319768    {{2},{1,2}}
%e A319768 4: {{1,1,1,1}}
%e A319768    {{1,1,2,2}}
%e A319768    {{1,2,2,2}}
%e A319768    {{1,2,3,3}}
%e A319768    {{1,2,3,4}}
%e A319768    {{1},{1,1,1}}
%e A319768    {{1},{1,2,2}}
%e A319768    {{2},{1,2,2}}
%e A319768    {{3},{1,2,3}}
%e A319768    {{1,2},{2,2}}
%e A319768    {{1},{2},{1,2}}
%Y A319768 Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616.
%Y A319768 Cf. A319752, A319765, A319766, A319767, A319769, A319773, A319774.
%K A319768 nonn,more
%O A319768 0,3
%A A319768 _Gus Wiseman_, Sep 27 2018