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.



Solving a recursive formula
These are called Mahonian numbers, according to OEIS. <https://oeis.org/A008302>


