Factorial Summation

Calculus Level 5

$\large \sum_{n=0}^\infty\sum_{r=0}^\infty\sum_{k=0}^\infty\dfrac{n!r!k!}{(n+r+k+2)!}$

The above sum can be written as $$\dfrac{\pi^a}{b}$$ for positive integers $$a$$ and $$b$$. Evaluate $$a+b$$

×