Level
3

Evaluate

$\sum_{a=0}^\infty \sum_{b=0}^\infty \sum_{c=0}^a \sum_{d=0}^b \sum_{e=0}^d {n+a \choose a} {b-e \choose d-e} {a \choose c} {b \choose e} (-1)^{b+c} n^e c^{d-e}$

Now before you enter your final answer -

If your final answer is a rational number and is in the form $\frac{p}{q}$ where $p$ and $q$ are coprime to each other then your final answer should be $\frac{p\pi}{q}$.

Otherwise If your final answer is an irrational number then your final answer should be $99$

It is an entry in the Troll King Contest.