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factcomb-minfactorial-ratsimp

solve_rec(a[n]=a[n-1]...

2*x*(x+1)*y[x] - (x^...

solve_rec(%, y[x], y...

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factcomb-false-rat-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

rat(q);

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factcomb-false-sumsplitfact

f(n,k):=n!^2/(k!*(n-k...

p: factcomb(f(n,k)-(n...

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factcomb-false-sumsplitfact

f(n,k):=n!^2/(k!*(n-k...

p: factcomb(f(n,k)-(n...

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factcomb-false-rat-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

rat(q);

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factcomb-false-sumsplitfact

f(n,k):=n!^3/(k!*(n-k...

p: factcomb(f(n,k)-(n...

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factcomb-false-rat-sumsplitfact

f(n,k):=n!^3/(k!^3*(n...

sumsplitfact:false;

p: factcomb(rat(f(n,k...

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factcomb-pochhammer

factcomb(pochhammer(a...

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factcomb-false-num-rat-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

num(q);

Calculate

factcomb-false-sumsplitfact

p: (n-1)!/((k-1)!*(n-...

q: factcomb(p*(k-2)!*...

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factcomb

Run Example
(%i1)factcomb(3/(x+y)^2 - 4/(x-y)^2 + 5/(x^2-y^2));
                            5         3          4
(%o1)                    ------- + -------- - --------
                          2    2          2          2
                         x  - y    (y + x)    (x - y)
(%i2) 
Run Example
p: (n-1)!/((k-1)!*(n-k)!)-k*(n-2)!/((k-1)!*(n-k-1)!)-(n-2)!/((k-2)!*(n-k)!);
             (n - 1)!            (n - 2)!             k (n - 2)!
(%o1)    ----------------- - ----------------- - ---------------------
         (k - 1)! (n - k)!   (k - 2)! (n - k)!   (k - 1)! (n - k - 1)!
(%i2) q: factcomb(p*(k-2)!*(n-k-1)!/(n-2)!), sumsplitfact:false;
                             n - 1          1       k
(%o2)                   --------------- - ----- - -----
                        (k - 1) (n - k)   n - k   k - 1
(%i3) num(q);
                             n - 1          1       k
(%o3)                   --------------- - ----- - -----
                        (k - 1) (n - k)   n - k   k - 1
(%i4) rat(q);
(%o4)/R/                              - 1
(%i5) 
Run Example
f(n,k):=n!^3/k!^3*(n-k)!^3;
                                        3
                                      n!          3
(%o1)                      f(n, k) := --- (n - k)!
                                        3
                                      k!
(%i2) sumsplitfact:false;
(%o2)                                false
(%i3) p: factcomb(f(n,k)-(n^2+n*k+k^2)/(n-k)^2*f(n-1,k)-f(n-1,k-1));
              5        3         3             3
             n  (n - k)  (n - 1)!  (n - k - 1)!
(%o3) -------------------------------------------------
       3         3  2      4         3      5         3
      k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
             4        3         3             3
        2 k n  (n - k)  (n - 1)!  (n - k - 1)!
 - -------------------------------------------------
    3         3  2      4         3      5         3
   k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
         2  3        3         3             3
        k  n  (n - k)  (n - 1)!  (n - k - 1)!
 + -------------------------------------------------
    3         3  2      4         3      5         3
   k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
               2         3             3
              n  (n - 1)!  (n - k - 1)!
 - -------------------------------------------------
    3         3  2      4         3      5         3
   k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
                          3             3
              k n (n - 1)!  (n - k - 1)!
 - -------------------------------------------------
    3         3  2      4         3      5         3
   k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
               2         3             3
              k  (n - 1)!  (n - k - 1)!
 - -------------------------------------------------
    3         3  2      4         3      5         3
   k  (k - 1)!  n  - 2 k  (k - 1)!  n + k  (k - 1)!
          3         3             3
   (n - k)  (n - 1)!  (n - k - 1)!
 - --------------------------------
                      3
              (k - 1)!
(%i4) 

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