I am familiar with the standard proof that the binomial coefficient is an integer based on induction and Pascal's Rule.

I'm trying to prove that a related expression is an integer:

$\displaystyle f(m, n) = \frac{(m + n)!}{m!n!}$

Using an adaptation of Pascal's Rule, we can see that $\displaystyle f(m,n) + f(m+1,n-1) = f(m+1,n)$ and $\displaystyle f(m - 1,n) + f(m,n - 1) = f(m,n)$, but these equalities don't lead to an inductive proof.