I have this recursive equation:

$$\begin{align*} F(m,n)=F&=F(m,n-1)+F(m-1,n)-F(m-1,n-1-m) \\\\ F(m,0)&=F\left(m,m(m+1)/2\right)=1\\ F(m,i)=0&=0\text{ if i<0, i> }i<0\text{ or }i>\frac12m(m+1) \end{align*}$$

is there a way to solve this recursive equation to get a close form for F $F(m,n)$

I have tried z transform, but I got nothing