I'm preparing myself for discrete math exam, and I have no problem when dealing with simple sum, but when I see a monstrous one I totally don't know what to do. Here's an example:

$$\sum\_{1\leq i < j \leq m}\sum\_{1\leq k,l \leq n}[k+l\leq n]\binom{n}{k}\binom{n-k}{l}(j-i-1)^{n-k-l}$$ for $m,n > 0$.

I need to simplify this sum. Binomial coefficients suggest we can think of this cominatorically but I'm totally stuck. Are there any general techniques helpful when dealing with such sums?