# Some Triple Sum

Calculus Level 5

$\large \sum_{i=0}^{\infty} \sum_{j=0}^{\infty} \sum_{k=0}^{\infty} \frac{i! j! k!}{(i+j+k+2)!}$

If the value of the summation above is equal to $$\dfrac{\pi^A}{B}$$ for integers $$A$$ and $$B$$, find the value of $$B - A$$.

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