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A319790
Number of non-isomorphic connected multiset partitions of weight n with empty intersection.
5
1, 0, 0, 0, 1, 5, 32, 134, 588, 2335, 9335, 36506, 144263, 571238, 2291894, 9300462, 38303796, 160062325, 679333926, 2927951665, 12817221628, 56974693933, 257132512297, 1177882648846, 5475237760563, 25818721638720, 123473772356785, 598687942799298, 2942344764127039
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) = A007718(n) - A007716(n) + A317757(n). - Andrew Howroyd, May 31 2023
EXAMPLE
Non-isomorphic representatives of the a(4) = 1 through a(5) = 5 connected 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}}
{{1},{2},{2},{1,2}}
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 27 2018
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, May 31 2023
STATUS
approved