The asymptotic expansion, w.r.t. t, to, order 3, of the 2r-th moment

                            (about the mean) of the

          r.v. Number of inversions for words with a*t 1's and b*t 2's

            Here a,b,t, and r are symbolic(!), only s is numeric. is

       /                  2                                2
       |      r (-1 + r) b    r (-6 + r) a b   r (-1 + r) a
       |    - ------------- - -------------- - -------------   /
 (3 r) |            5               5                5         |
t      |1 + ------------------------------------------------ + |
       \                     t a b (a + b)                     \

                                    4                   2                  3
    r (-1 + r) (r - 2) (21 r + 17) b    r (-1 + r) (21 r  - 130 r - 34) a b
    --------------------------------- + ------------------------------------
                  1050                                  525

                       2               2  2
       r (-1 + r) (21 r  - 95 r + 71) a  b
     + ------------------------------------
                       350

                       2                3                                     4
       r (-1 + r) (21 r  - 130 r - 34) a  b   r (-1 + r) (r - 2) (21 r + 17) a
     + ------------------------------------ + ---------------------------------
                       525                                  1050

    \                           /   2                                      6
    |   /   2  2  2        2    |  r  (-1 + r) (r - 2) (r - 3) (7 r + 17) b
    |  /  (t  a  b  (a + b) ) + |- -----------------------------------------
    / /                         \                    5250

        2                       2                   5
       r  (-1 + r) (r - 2) (21 r  - 117 r - 238) a b
     - ----------------------------------------------
                            5250

                       4        3        2                 2  4
       r (-1 + r) (42 r  - 318 r  + 367 r  + 577 r + 300) a  b
     - --------------------------------------------------------
                                 5250

                       4        3        2                 3  3
       r (-1 + r) (49 r  - 441 r  + 509 r  + 924 r + 960) a  b
     - --------------------------------------------------------
                                 5250

                       4        3        2                 4  2
       r (-1 + r) (42 r  - 318 r  + 367 r  + 577 r + 300) a  b
     - --------------------------------------------------------
                                 5250

        2                       2                 5
       r  (-1 + r) (r - 2) (21 r  - 117 r - 238) a  b
     - ----------------------------------------------
                            5250

                                                                         \
                                                                         |
        2                                      6\                        |
       r  (-1 + r) (r - 2) (r - 3) (7 r + 17) a |   /   3  3  3        3 |
     - -----------------------------------------|  /  (t  a  b  (a + b) )|
                         5250                   / /                      /

           /a b (a + b)\r   /      r
    (2 r)! |-----------|   /  (r! 2 )
           \    12     /  /

                This all things too, 7.545, seconds of CPU time