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A320665 Number of non-isomorphic multiset partitions of weight n with no singletons or vertices that appear only once. 3
1, 0, 1, 1, 5, 6, 27, 47, 169, 406, 1327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The dual of a multiset partition has, for each vertex, one part consisting of the indices (or positions) of the parts containing that vertex, counted with multiplicity. For example, the dual of {{1,2},{2,2}} is {{1},{1,2,2}}. This sequence counts non-isomorphic multiset partitions with no singletons whose dual also has no singletons.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(2) = 1 through a(6) = 27 multiset partitions:

  {{1,1}}  {{1,1,1}}  {{1,1,1,1}}    {{1,1,1,1,1}}    {{1,1,1,1,1,1}}

                      {{1,1,2,2}}    {{1,1,2,2,2}}    {{1,1,1,2,2,2}}

                      {{1,1},{1,1}}  {{1,1},{1,1,1}}  {{1,1,2,2,2,2}}

                      {{1,1},{2,2}}  {{1,1},{1,2,2}}  {{1,1,2,2,3,3}}

                      {{1,2},{1,2}}  {{1,1},{2,2,2}}  {{1,1},{1,1,1,1}}

                                     {{1,2},{1,2,2}}  {{1,1,1},{1,1,1}}

                                                      {{1,1},{1,2,2,2}}

                                                      {{1,1,1},{2,2,2}}

                                                      {{1,1,2},{1,2,2}}

                                                      {{1,1},{2,2,2,2}}

                                                      {{1,1,2},{2,2,2}}

                                                      {{1,1},{2,2,3,3}}

                                                      {{1,1,2},{2,3,3}}

                                                      {{1,2},{1,1,2,2}}

                                                      {{1,2},{1,2,2,2}}

                                                      {{1,2},{1,2,3,3}}

                                                      {{1,2,2},{1,2,2}}

                                                      {{1,2,3},{1,2,3}}

                                                      {{2,2},{1,1,2,2}}

                                                      {{1,1},{1,1},{1,1}}

                                                      {{1,1},{1,2},{2,2}}

                                                      {{1,1},{2,2},{2,2}}

                                                      {{1,1},{2,2},{3,3}}

                                                      {{1,1},{2,3},{2,3}}

                                                      {{1,2},{1,2},{1,2}}

                                                      {{1,2},{1,2},{2,2}}

                                                      {{1,2},{1,3},{2,3}}

CROSSREFS

Cf. A001055, A007716, A306005, A317794, A318871, A320663, A320664.

Sequence in context: A022165 A022163 A048060 * A303731 A298175 A298144

Adjacent sequences:  A320662 A320663 A320664 * A320666 A320667 A320668

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Oct 18 2018

STATUS

approved

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Last modified July 17 08:42 EDT 2019. Contains 325098 sequences. (Running on oeis4.)