I'm trying to automatically solve a recurrence formula with more than one variable. Here is an example:
$$t(n,k) = t(n-1,k-1) + t(n-1,k)$$
The answer I expect is: $$ t(n,k) = \binom{n}{k} $$ When I try it with maple nothing happens, and it simply repeats what I wrote:
$$\text{rsolve}(f(n, k) = f(n - 1, k - 1) + f(n - 1, k), f(n, k))$$
Any way to automatically solve such recurrences? with maple? or other tool?