

A319558


The squarefree dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted without multiplicity. Then a(n) is the number of nonisomorphic multiset partitions of weight n whose squarefree dual is strict (no repeated blocks).


33



1, 1, 3, 7, 21, 55, 169, 496, 1582, 5080, 17073
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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.


LINKS

Table of n, a(n) for n=0..10.


EXAMPLE

Nonisomorphic representatives of the a(1) = 1, a(2) = 3, and a(3) = 7 multiset partitions:
1: {{1}}
2: {{1,1}}
{{1},{1}}
{{1},{2}}
3: {{1,1,1}}
{{1},{1,1}}
{{1},{2,2}}
{{2},{1,2}}
{{1},{1},{1}}
{{1},{2},{2}}
{{1},{2},{3}}


CROSSREFS

Cf. A007716, A007718, A049311, A053419, A056156, A059201, A283877, A316980.
Cf. A319557, A319559, A319560, A319564, A319565, A319566, A319567.
Sequence in context: A192068 A318395 A151267 * A307251 A320803 A262184
Adjacent sequences: A319555 A319556 A319557 * A319559 A319560 A319561


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Sep 23 2018


STATUS

approved



