How to calculate the sum of general type 
$$\sum_{k=0}^n {n\choose k} {n\choose k+a} {2 l - n + a \choose r } $$ ?

Some particular examples 
$$\sum_{k=0}^n {n\choose k} {n\choose k+a}  = {2n\choose n+a}$$,
$$\sum_{k=0}^n {n\choose k} {n\choose k+a} (2 l - n + a) = 0 $$,
$$\sum_{k=0}^n {n\choose k} {n\choose k+a} {2 l - n + a \choose 2}  = \frac{(a+ n)(a-n)}{2 (1-2 n)} {2n\choose n+a} $$,
$$\sum_{k=0}^n {n\choose k} {n\choose k+a} {2 l - n + a \choose 3}  = - \frac{(a+ n)(a-n)}{2 (1-2 n)} {2n\choose n+a} $$ .
I am struggling to calculate at least 
$$\sum_{k=0}^n {n\choose k} {n\choose k+a} {2 l - n + a \choose 4}  = ? $$
Can someone  help me with this one?