I would like to solve this recurrence relation:
$a_{m,n}=a_{m-1,n}+a_{m,n-1}$
with
$a_{0,0}=0, a_{m,0}=1, a_{0,n}=1$ for all $m\neq0$ and $n\neq0$
That's resembles the Tartaglia/Pascal's triangle,
the solution should be just the combinations... $a_{m,n}=\binom{m+n}{n}$
But when I try to solve it with Mathematica
RSolve[{a[m, n] == a[-1 + m, n] + a[m, -1 + n],a[0, 0] == 0,
a[m, 0] == 1, a[0, n] == 1}, a[m, n], {m, n}]
It just outputs the same input unevaluated.
What am I doing wrong?
Euler recurrence equation is also unsolved.
