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 A319558 The squarefree dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted without multiplicity. Then a(n) is the number of non-isomorphic multiset partitions of weight n whose squarefree dual is strict (no repeated blocks). 33
 1, 1, 3, 7, 21, 55, 169, 496, 1582, 5080, 17073 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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, a(2) = 3, and a(3) = 7 multiset partitions: 1:    {{1}} 2:   {{1,1}}     {{1},{1}}     {{1},{2}} 3:  {{1,1,1}}    {{1},{1,1}}    {{1},{2,2}}    {{2},{1,2}}   {{1},{1},{1}}   {{1},{2},{2}}   {{1},{2},{3}} CROSSREFS Cf. A007716, A007718, A049311, A053419, A056156, A059201, A283877, A316980. Cf. A319557, A319559, A319560, A319564, A319565, A319566, A319567. Sequence in context: A192068 A318395 A151267 * A307251 A320803 A262184 Adjacent sequences:  A319555 A319556 A319557 * A319559 A319560 A319561 KEYWORD nonn,more AUTHOR Gus Wiseman, Sep 23 2018 STATUS approved

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Last modified May 29 10:05 EDT 2020. Contains 334699 sequences. (Running on oeis4.)