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, 2, 4, 9, 19, 49, 115, 310, 830, 2383

Offset: 0

Author

Gus Wiseman, Aug 15 2019

Keywords

• nonn
• more

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.

Examples

			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.