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
Andrew Howroyd, Table of n, a(n) for n = 0..50
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}}
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 23 2018
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Jan 19 2023
STATUS
approved