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A319793
Number of non-isomorphic connected strict multiset partitions (sets of multisets) of weight n with empty intersection.
1
1, 0, 0, 0, 1, 4, 24, 96, 412, 1607, 6348, 24580, 96334, 378569, 1508220, 6079720, 24879878, 103335386, 436032901, 1869019800, 8139613977, 36008825317, 161794412893, 738167013847, 3418757243139, 16068569129711, 76622168743677, 370571105669576, 1817199912384794
OFFSET
0,6
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
FORMULA
a(n) = A319557(n) - A316980(n) + A319077(n). - Andrew Howroyd, May 31 2023
EXAMPLE
Non-isomorphic representatives of the a(4) = 1 through a(5) = 4 multiset partitions:
4: {{1},{2},{1,2}}
5: {{1},{2},{1,2,2}}
{{1},{1,2},{2,2}}
{{2},{3},{1,2,3}}
{{2},{1,3},{2,3}}
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 27 2018
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, May 31 2023
STATUS
approved