### Related

##### minfactorial

f(n):=(b+n)!/(a+n)!;

f(n+1)/f(n);

minfactorial(f(n+1)/f...

Calculate

? minfactorial;

Calculate

##### minfactorial

n!/(n+2)!;

minfactorial (%);

Calculate

##### minfactorial

f(n):=(b+n)!/(a+n)!;

f(n+1)/f(n);

minfactorial(f(n+1)/f...

Calculate

? minfactorial;

Calculate

##### minfactorial

n!/(n+2)!;

minfactorial (%);

Calculate

### minfactorial

Run Example
```(%i1)f(n,k):=n!*n!/(n*k!*(n-k)!*(k-1)!*(n-k+1)!);
n! n!
(%o1)           f(n, k) := -----------------------------------
n k! (n - k)! (k - 1)! (n - k + 1)!
(%i2) makefact:true;
(%o2)                                true
(%i3) facexpand: true, factorial_expand: true;
(%o3)                                true
(%i4) eq: num(rat(A*minfactorial(f(n-1,k)/f(n,k))+B*minfactorial(f(n-1,k-1)/f(n,k))-1));
2            2                    2           2
(%o4)/R/     (k  - k) B + (n  + (- 2 k + 1) n + k  - k) A - n  + n
(%i5) eq: rat(expand(eq),n);
2                             2            2
(%o5)/R/ (A - 1) n  + ((- 2 k + 1) A + 1) n + (k  - k) B + (k  - k) A
(%i6) subst(a1*n+a2*k+a3,A,eq);
2
(%o6) (k  - k) B + n ((1 - 2 k) (a1 n + a2 k + a3) + 1)
2                            2
+ (k  - k) (a1 n + a2 k + a3) + n  (a1 n + a2 k + a3 - 1)
(%i7) ```
Run Example
```f(k):=(2*n)!/(k!*(2*n-k)!)*a^(2*n-k)*b^k;
(2 n)!      2 n - k  k
(%o1)                  f(k) := ------------- a        b
k! (2 n - k)!
(%i2) facexpand: true, factorial_expand: true;
(%o2)                                true
(%i3) f(k+1)/f(k);
b k! (2 n - k)!
(%o3)                      -------------------------
a (k + 1)! (2 n - k - 1)!
(%i4) minfactorial(f(k+1)/f(k));
b (2 n - k)
(%o4)                             -----------
a (k + 1)
(%i5) eq: sum(f(kk),kk,0,n);
n
====     2 n - kk  kk
\       a         b
(%o5)                    (2 n)!  >     ---------------
/      kk! (2 n - kk)!
====
kk = 0
(%i6) solve_rec();
(%o6)                             solve_rec()
(%i7) ```
Run Example
```f(j):=binomial(k,j)*3^(k-j)*gamma(k/2+j+a)/gamma(k/2+j);
k - j       k
binomial(k, j) 3      gamma(- + j + a)
2
(%o1)           f(j) := --------------------------------------
k
gamma(- + j)
2
(%i2) minfactorial(makefact(f(j+1)/f(j)));
k
(- + j + a) (k - j)
2
(%o2)                         -------------------
k
3 (j + 1) (- + j)
2
(%i3) ```

### Related Help

Help for Minfactorial