

A319631


Number of nonisomorphic weightn antichains of multisets whose dual is a chain of distinct multisets.


0



1, 1, 2, 3, 5, 5, 13, 11, 25, 31, 54
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OFFSET

0,3


COMMENTS

The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}.
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 through a(5) = 5 antichains:
1: {{1}}
2: {{1,1}}
{{1},{1}}
3: {{1,1,1}}
{{1,2,2}}
{{1},{1},{1}}
4: {{1,1,1,1}}
{{1,2,2,2}}
{{1,1},{1,1}}
{{1,2},{2,2}}
{{1},{1},{1},{1}}
5: {{1,1,1,1,1}}
{{1,1,2,2,2}}
{{1,2,2,2,2}}
{{1,2},{2,2,2}}
{{1},{1},{1},{1},{1}}


CROSSREFS

Cf. A000219, A006126, A007716, A059201, A293606, A316980, A316983, A318099, A319558, A319616A319646, A300913.
Sequence in context: A156834 A079024 A342421 * A097453 A079125 A146305
Adjacent sequences: A319628 A319629 A319630 * A319632 A319633 A319634


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Sep 25 2018


STATUS

approved



