Let f_n(x) be the generating function of Sum of (Chi{n-1,1)+1)^k  with Chi_m\
    u for all mu

Then it follows from the character table (probably) that the denominator is \
    predicible



                                  /  n - 3              \
                                  | --------'           |
                                  |'  |  |              |
                       (-n x + 1) |   |  |    (-i x + 1)|
                                  |   |  |              |
                                  |   |  |              |
                                  \  i = 1              /



      Hence the numerator is a polynomial of degree n-2 and can be written



                                n - 2
                                -----
                                 \             i
                                  )   P[i](n) x
                                 /
                                -----
                                i = 0



      where we conjecture that P[i](n) is a polynomial of n of degree 2*i


                                             3
                      The numerator, up to, x , starts as

    (n - 1) (n - 2) x   /     4         3        2   25      \  2
1 - ----------------- + |1/8 n  - 5/12 n  + 3/8 n  - -- n + 5| x
            2           \                            12      /

       /       6         5         4   47  3   61  2              \  3
     + |-1/48 n  + 1/48 n  + 1/16 n  + -- n  - -- n  - 11/2 n + 17| x
       \                               48      24                 /



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