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A319557
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Number of non-isomorphic strict connected multiset partitions of weight n.
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29
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1, 1, 2, 5, 12, 30, 91, 256, 823, 2656, 9103, 31876, 116113, 432824, 1659692, 6508521, 26112327, 106927561, 446654187, 1900858001, 8236367607, 36306790636, 162724173883, 741105774720, 3428164417401, 16099059101049, 76722208278328, 370903316203353, 1818316254655097
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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.
Also the number of non-isomorphic connected T_0 multiset partitions of weight n. In a multiset partition, two vertices are equivalent if in every block the multiplicity of the first is equal to the multiplicity of the second. The T_0 condition means that there are no equivalent vertices.
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LINKS
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FORMULA
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Inverse Euler transform of A316980.
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EXAMPLE
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Non-isomorphic representatives of the a(4) = 12 strict connected multiset partitions:
{{1,1,1,1}}
{{1,1,2,2}}
{{1,2,2,2}}
{{1,2,3,3}}
{{1,2,3,4}}
{{1},{1,1,1}}
{{1},{1,2,2}}
{{2},{1,2,2}}
{{3},{1,2,3}}
{{1,2},{2,2}}
{{1,3},{2,3}}
{{1},{2},{1,2}}
Non-isomorphic representatives of the a(4) = 12 connected T_0 multiset partitions:
{{1,1,1,1}}
{{1,2,2,2}}
{{1},{1,1,1}}
{{1},{1,2,2}}
{{2},{1,2,2}}
{{1,1},{1,1}}
{{1,2},{2,2}}
{{1,3},{2,3}}
{{1},{1},{1,1}}
{{1},{2},{1,2}}
{{2},{2},{1,2}}
{{1},{1},{1},{1}}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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