

A319619


Number of nonisomorphic connected weightn antichains of multisets whose dual is also an antichain of multisets.


0



1, 1, 3, 3, 6, 4, 15, 13, 48, 96, 280
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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.


FORMULA

Euler transform is A318099.


EXAMPLE

Nonisomorphic representatives of the a(1) = 1 through a(5) = 4 antichains:
1: {{1}}
2: {{1,1}}
{{1,2}}
{{1},{1}}
3: {{1,1,1}}
{{1,2,3}}
{{1},{1},{1}}
4: {{1,1,1,1}}
{{1,1,2,2}}
{{1,2,3,4}}
{{1,1},{1,1}}
{{1,2},{1,2}}
{{1},{1},{1},{1}}
5: {{1,1,1,1,1}}
{{1,2,3,4,5}}
{{1,1},{1,2,2}}
{{1},{1},{1},{1},{1}}


CROSSREFS

Cf. A006126, A007716, A007718, A056156, A059201, A316980, A316983, A318099, A319557, A319558, A319565, A319616A319646, A300913.
Sequence in context: A137462 A163926 A050346 * A309001 A142149 A132119
Adjacent sequences: A319616 A319617 A319618 * A319620 A319621 A319622


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Sep 25 2018


STATUS

approved



