What is the solve of F(n,n) = F(n-1,n) + F(n, n-1) + 1 Where F(0,a) = 1 and F(a, 0) = 1 for every a
Your function produces the sequence A109128, that is
$$
\mathit{recurser}(i,j) = 2\binom{i+j}{i} - 1.
$$
You can prove this by induction.
How I found out: I computed the first few values, and searched the OEIS.