These are comparative timings  of the functions in the Maple package JumpMod\
    el.txt

The time it takes to compute allsequence, p_{ij}(t) for 1<=i,j<=, 100,

    using Eq. (15) is



                                     4.487

The time it takes to compute these using the recurrence found by the Zeilber\
    ger algorithm is

                                     2.048

The time it takes to compute the first, 100, terms using Eq. (16) and the ori\
    ginal expression for p_{ij}(t) given by Eq. (15) is

                                    150.205

 The time it takes to compute the first, 100, terms using the pijtF(i,j,t)  is

                                     45.079

The time it takes to compute the first, 100,

    terms using the recurrence found by the guessed recurrence is

                                     0.063