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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, enter image description here

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.

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  • $\begingroup$ I don't think Mathematica supports bivariate (or multivariate in general) sequences in RSolve... See also stackoverflow.com/questions/42751561/… . $\endgroup$ – user45207 Dec 9 '17 at 18:13
  • $\begingroup$ That question is mine too. I wrote this new one because the older wasn't solved either. I expected Mathematica could solve it (It's supposed to be a very capable software). Is any other CAS able to do it? $\endgroup$ – skan Dec 10 '17 at 20:24

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