> restart:
> q := 1 - p;
> np := n * p;
> r := p / q;
> g := r * (n + 1);
> f:=q^n;
> factor(g / k - r);
> for i from 1 to 10 do
>   f := factor(f * (g / i - r));
> od;

                              q := 1 - p


                              np := n p


                                     p
                              r := -----
                                   1 - p


                                 p (n + 1)
                            g := ---------
                                   1 - p


                                        n
                            f := (1 - p)


                             p (n + 1 - k)
                           - -------------
                              (-1 + p) k


                                       n
                                (1 - p)  n p
                         f := - ------------
                                   -1 + p


                                  n    2
                           (1 - p)  n p  (n - 1)
                      f := ---------------------
                                          2
                                2 (-1 + p)


                               n    3
                        (1 - p)  n p  (n - 1) (n - 2)
                 f := - -----------------------------
                                           3
                                 6 (-1 + p)


                          n    4
                   (1 - p)  n p  (n - 1) (n - 2) (n - 3)
              f := -------------------------------------
                                          4
                               24 (-1 + p)


                       n    5
                (1 - p)  n p  (n - 1) (n - 2) (n - 3) (n - 4)
         f := - ---------------------------------------------
                                            5
                                120 (-1 + p)


                  n    6
           (1 - p)  n p  (n - 1) (n - 2) (n - 3) (n - 4) (n - 5)
      f := -----------------------------------------------------
                                           6
                               720 (-1 + p)


                n    7
  f := - (1 - p)  n p  (n - 1) (n - 2) (n - 3) (n - 4) (n - 5)

                  /               7
        (n - 6)  /  (5040 (-1 + p) )
                /


              n    8
  f := (1 - p)  n p  (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (n - 6)

                  /                8
        (n - 7)  /  (40320 (-1 + p) )
                /


                n    9
  f := - (1 - p)  n p  (n - 1) (n - 2) (n - 3) (n - 4) (n - 5)

                                  /                 9
        (n - 6) (n - 7) (n - 8)  /  (362880 (-1 + p) )
                                /


              n    10
  f := (1 - p)  n p   (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) (n - 6)

                                  /                  10
        (n - 7) (n - 8) (n - 9)  /  (3628800 (-1 + p)  )
                                /

> 100!;

  9332621544394415268169923885626670049071596826438162146859296389\
        5217599993229915608941463976156518286253697920827223758251\
        185210916864000000000000000000000000

> 
