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A321255 Number of connected multiset partitions with multiset density -1, of strongly normal multisets of size n, with no singletons. 3
0, 0, 2, 3, 8, 19, 60, 183, 643, 2355, 9393 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The multiset density of a multiset partition is the sum of the numbers of distinct vertices in each part minus the number of parts minus the number of vertices.

A multiset is normal if it spans an initial interval of positive integers, and strongly normal if in addition its multiplicities are weakly decreasing.

LINKS

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

EXAMPLE

The a(2) = 2 through a(5) = 19 multiset partitions:

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

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

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

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

                      {{1,2,3,4}}    {{1,1,2,2,3}}

                      {{1,1},{1,1}}  {{1,1,2,3,4}}

                      {{1,1},{1,2}}  {{1,2,3,4,5}}

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

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

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

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

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

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

                                     {{1,2},{1,3,4}}

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

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

                                     {{1,3},{1,2,4}}

                                     {{1,4},{1,2,3}}

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

CROSSREFS

Cf. A000272, A030019, A052888, A134954, A304867, A317672, A321228, A321229, A321253.

Sequence in context: A077269 A294431 A148043 * A243791 A243335 A303835

Adjacent sequences:  A321252 A321253 A321254 * A321256 A321257 A321258

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Nov 01 2018

STATUS

approved

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Last modified July 23 14:36 EDT 2019. Contains 325255 sequences. (Running on oeis4.)