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A327481 Triangle read by rows where T(n,k) is the number of nonempty subsets of {1..n} with mean k. 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

All terms are odd.

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

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}

MATHEMATICA

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

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.

Sequence in context: A157454 A106255 A143086 * A152714 A174546 A134444

Adjacent sequences:  A327478 A327479 A327480 * A327482 A327483 A327484

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Sep 13 2019

STATUS

approved

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Last modified May 11 12:47 EDT 2021. Contains 343791 sequences. (Running on oeis4.)