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A319619 Number of non-isomorphic connected weight-n antichains of multisets whose dual is also an antichain of multisets. 0
1, 1, 3, 3, 6, 4, 15, 13, 48, 96, 280 (list; graph; refs; listen; history; text; internal format)
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

Non-isomorphic 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, A319616-A319646, 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

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Last modified April 19 00:03 EDT 2021. Contains 343098 sequences. (Running on oeis4.)