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 A319766 Number of non-isomorphic strict intersecting multiset partitions (sets of multisets) of weight n whose dual is also a strict intersecting multiset partition. 6
 1, 1, 1, 4, 6, 14, 31, 64, 145, 324, 753 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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}}. 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. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. LINKS EXAMPLE Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset partitions: 1: {{1}} 2: {{1,1}} 3: {{1,1,1}}    {{1,2,2}}    {{1},{1,1}}    {{2},{1,2}} 4: {{1,1,1,1}}    {{1,2,2,2}}    {{1},{1,1,1}}    {{1},{1,2,2}}    {{2},{1,2,2}}    {{1,2},{2,2}} 5: {{1,1,1,1,1}}    {{1,1,2,2,2}}    {{1,2,2,2,2}}    {{1},{1,1,1,1}}    {{1},{1,2,2,2}}    {{2},{1,1,2,2}}    {{2},{1,2,2,2}}    {{2},{1,2,3,3}}    {{1,1},{1,1,1}}    {{1,1},{1,2,2}}    {{1,2},{1,2,2}}    {{1,2},{2,2,2}}    {{2,2},{1,2,2}}    {{2},{1,2},{2,2}} CROSSREFS Cf. A007716, A281116, A283877, A305854, A306006,  A316980, A316983, A317757, A319616. Cf. A319752, A319765, A319767, A319768, A319769, A319773, A319774. Sequence in context: A005202 A342602 A106526 * A108516 A219774 A274208 Adjacent sequences:  A319763 A319764 A319765 * A319767 A319768 A319769 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 27 2018 STATUS approved

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Last modified August 19 18:30 EDT 2022. Contains 356229 sequences. (Running on oeis4.)