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A327017 Number of non-isomorphic multiset partitions of weight n where every vertex, as a multiset of weight 1, is the multiset-meet of some subset of the edges. 1
1, 1, 2, 4, 9, 19, 49, 115, 310, 830, 2383 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The multiset-meet of a collection of multisets has as underlying set the intersection of their underlying sets and as multiplicities the minima of their multiplicities.

LINKS

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

EXAMPLE

Non-isomorphic representatives of the a(1) = 1 through a(5) = 19 multiset partitions:

    {1}  {1}{1}  {1}{11}    {1}{111}      {1}{1111}

         {1}{2}  {1}{1}{1}  {1}{1}{11}    {1}{1}{111}

                 {1}{2}{2}  {1}{2}{12}    {1}{11}{11}

                 {1}{2}{3}  {1}{2}{22}    {1}{12}{22}

                            {1}{1}{1}{1}  {1}{2}{122}

                            {1}{1}{2}{2}  {1}{2}{222}

                            {1}{2}{2}{2}  {1}{1}{1}{11}

                            {1}{2}{3}{3}  {1}{1}{2}{22}

                            {1}{2}{3}{4}  {1}{2}{2}{12}

                                          {1}{2}{2}{22}

                                          {1}{2}{3}{23}

                                          {1}{2}{3}{33}

                                          {1}{1}{1}{1}{1}

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

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

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

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

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

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

CROSSREFS

Cf. A007716, A059523, A326961, A326965, A326967, A326972, A326974, A326976, A326977, A326979, A327012.

Sequence in context: A133228 A036717 A000080 * A153447 A076893 A176501

Adjacent sequences:  A327014 A327015 A327016 * A327018 A327019 A327020

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 15 2019

STATUS

approved

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Last modified May 31 15:41 EDT 2020. Contains 334748 sequences. (Running on oeis4.)