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

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

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