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A319558
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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).
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33
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1, 1, 3, 7, 21, 55, 169, 496, 1582, 5080, 17073
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OFFSET
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0,3
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COMMENTS
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The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
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LINKS
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EXAMPLE
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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}}
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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