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 A319779 Number of intersecting multiset partitions of weight n whose dual is not an intersecting multiset partition. 16
 1, 0, 0, 0, 1, 4, 20, 66, 226, 696, 2156 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 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}}. The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices. 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. LINKS EXAMPLE Non-isomorphic representatives of the a(4) = 1 through a(6) = 20 multiset partitions: 4: {{1,3},{2,3}} 5: {{1,2},{2,3,3}}    {{1,3},{2,3,3}}    {{1,4},{2,3,4}}    {{3},{1,3},{2,3}} 6: {{1,2},{2,3,3,3}}    {{1,3},{2,2,3,3}}    {{1,3},{2,3,3,3}}    {{1,3},{2,3,4,4}}    {{1,4},{2,3,4,4}}    {{1,5},{2,3,4,5}}    {{1,1,2},{2,3,3}}    {{1,2,2},{2,3,3}}    {{1,2,3},{3,4,4}}    {{1,2,4},{3,4,4}}    {{1,2,5},{3,4,5}}    {{1,3,3},{2,3,3}}    {{1,3,4},{2,3,4}}    {{2},{1,2},{2,3,3}}    {{3},{1,3},{2,3,3}}    {{4},{1,4},{2,3,4}}    {{1,3},{2,3},{2,3}}    {{1,3},{2,3},{3,3}}    {{1,4},{2,4},{3,4}}    {{3},{3},{1,3},{2,3}} CROSSREFS Cf. A007716, A281116, A283877, A305854, A306006, A316980, A316983, A317757, A319616. Cf. A319775, A319778, A319781, A319783. Sequence in context: A194094 A055538 A302317 * A287244 A344993 A123613 Adjacent sequences:  A319776 A319777 A319778 * A319780 A319781 A319782 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 27 2018 STATUS approved

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Last modified May 20 11:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)