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

I have the following recursive formula: \begin{align} F(m,n) & = F(m,n - 1) + F(m - 1,n) - F(m - 1,n - 1 - m), \\ F(m,0) & = F \! \left( m,\frac{m (m + 1)}{2} \right) = 1, \\ F(m,i) & = 0 ~ \text{if} ~ i < 0 ~ \text{or} ~ i > \frac{m (m + 1)}{2}. \end{align} Is there a way to solve this recursive formula to obtain $ F(m,n) $ in closed form?

I tried the $ Z $-transform, but I got nothing.