A327481 Triangle read by rows where T(n,k) is the number of nonempty subsets of {1..n} with mean k.

1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 3, 7, 3, 1, 1, 3, 9, 9, 3, 1, 1, 3, 9, 19, 9, 3, 1, 1, 3, 9, 25, 25, 9, 3, 1, 1, 3, 9, 29, 51, 29, 9, 3, 1, 1, 3, 9, 31, 75, 75, 31, 9, 3, 1, 1, 3, 9, 31, 93, 151, 93, 31, 9, 3, 1, 1, 3, 9, 31, 105, 235, 235, 105, 31, 9, 3, 1

Offset: 1

Author

Gus Wiseman, Sep 13 2019

Keywords

• nonn
• tabl

Comments

All terms are odd.

Examples

			Triangle begins:
                         1
                       1   1
                     1   3   1
                   1   3   3   1
                 1   3   7   3   1
               1   3   9   9   3   1
             1   3   9  19   9   3   1
           1   3   9  25  25   9   3   1
         1   3   9  29  51  29   9   3   1
       1   3   9  31  75  75  31   9   3   1
     1   3   9  31  93 151  93  31   9   3   1
   1   3   9  31 105 235 235 105  31   9   3   1
The subsets counted in row n = 5:
  {1}  {2}      {3}          {4}      {5}
       {1,3}    {1,5}        {3,5}
       {1,2,3}  {2,4}        {3,4,5}
                {1,3,5}
                {2,3,4}
                {1,2,4,5}
                {1,2,3,4,5}
		

Crossrefs

Row sums are A051293.

The sequence of rows converges to A066571.

The version for partitions is A327482.

Cf. A000016, A063776, A065795, A135342, A327474, A327475, A327483, A327484.

Programs

Mathematica

Table[Length[Select[Subsets[Range[n]],Mean[#]==k&]],{n,10},{k,n}]