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A319557
Number of non-isomorphic strict connected multiset partitions of weight n.
29
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
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.
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.
LINKS
FORMULA
Inverse Euler transform of A316980.
EXAMPLE
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}}
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 23 2018
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 19 2023
STATUS
approved