A176725  W. Lang Apr 30 2010

Multiset choose 1 array MS(1;n,k)=a(n,k), k=1,..., A007294(n)

    Row nr. n       MS(1;n,k) list                                      list of multisets              
                                                                               
            1:       [1]                                                     [{1}]                                
                                                                               
            2:       [1]                                                     [{1,1}]                             

            3:       [2,1]                                                  [{1,2},{1,1,1}]                

            4:       [2,1]                                                  [{1,1,2},{1,1,1,1}]                   

            5:       [2,1]                                                  [{1, 1, 1, 2}, {1, 1, 1, 1, 1}]

            6:       [3,2,2,1]                                            [{1, 2, 3}, {1, 1, 2, 2}, {1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1}]

            7:       [3,2,2,1]                                            [{1, 1, 2, 3}, {1, 1, 1, 2, 2}, {1, 1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1, 1}]

            8:       [3,2,2,1]                                            [{1, 1, 1, 2, 3}, {1, 1, 1, 1, 2, 2}, {1, 1, 1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1, 1, 1}]

            9:       [3,3,2,2,2,1]                                      [{1, 1, 2, 2, 3}, {1, 1, 1, 1, 2, 3}, {1, 1, 1, 2, 2, 2}, {1, 1, 1, 1, 1, 2, 2},
                                                                         {1, 1, 1, 1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1}]  

           10:      [4,3,3,2,2,2,1]                                   [{1, 2, 3, 4}, {1, 1, 1, 2, 2, 3}, {1, 1, 1, 1, 1, 2, 3}, {1, 1, 1, 1, 2, 2, 2},
                                                                       {1, 1, 1, 1, 1, 1, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]

           11:      [4,3,3,2,2,2,1]                                   [{1, 1, 2, 3, 4}, {1, 1, 1, 1, 2, 2, 3}, {1, 1, 1, 1, 1, 1, 2, 3}, {1, 1, 1, 1, 1, 2, 2, 2}, 
                                                                      {1, 1, 1, 1, 1, 1, 1, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]              

           12:      [4,3,3,3,2,3,2,2,2,1]                          [{1, 1, 1, 2, 3, 4}, {1, 1, 2, 2, 3, 3}, {1, 1, 1, 2, 2, 2, 3}, {1, 1, 1, 1, 1, 2, 2, 3}, 
                                                                    {1, 1, 1, 1, 2, 2, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 2, 3}, {1, 1, 1, 1, 1, 1, 2, 2, 2}, 
                                                                    {1, 1, 1, 1, 1, 1, 1, 1, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]

           13:      [4,4,3,3,3,2,3,2,2,2,1]                       [{1, 1, 2, 2, 3, 4}, {1, 1, 1, 1, 2, 3, 4}, {1, 1, 1, 2, 2, 3, 3}, {1, 1, 1, 1, 2, 2, 2, 3}, 
                                                                   {1, 1, 1, 1, 1, 1, 2, 2, 3}, {1, 1, 1, 1, 1, 2, 2, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 2, 3},
                                                                   {1, 1, 1, 1, 1, 1, 1, 2, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2}, 
                                                                   {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]
 
           14:      [4,4,3,3,3,2,3,2,2,2,1]                       [{1, 1, 1, 2, 2, 3, 4}, {1, 1, 1, 1, 1, 2, 3, 4}, {1, 1, 1, 1, 2, 2, 3, 3}, {1, 1, 1, 1, 1, 2, 2, 2, 3}, 
                                                                   {1, 1, 1, 1, 1, 1, 1, 2, 2, 3}, {1, 1, 1, 1, 1, 1, 2, 2, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3}, 
                                                                   {1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2}, 
                                                                   {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}]

           15:     [5,4,3,4,3,3,3,2,3,2,3,2,2,2,1]            [{1, 2, 3, 4, 5}, {1, 1, 1, 1, 2, 2, 3, 4}, {1, 1, 1, 2, 2, 2, 3, 3}, {1, 1, 1, 1, 1, 1, 2, 3, 4}, 
                                                               {1, 1, 1, 1, 1, 2, 2, 3, 3}, {1, 1, 1, 1, 2, 2, 2, 2, 3}, {1, 1, 1, 1, 1, 1, 2, 2, 2, 3}, 
                                                               {1, 1, 1, 1, 1, 2, 2, 2, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3}, {1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2}, 
                                                               {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2},
                                                               {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}] 
        
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