This is weird

Calculus Level 5

Given that \[\displaystyle \large \sum _{a=0}^{\infty }\sum _{b=0}^{ \infty}\sum _{c=0}^{\infty }\frac{a^bb^c}{a!\times b!\times c!}=A\] Find \(\left\lfloor A \right\rfloor \).


For the purpose of this question, assume \(0^0=1\)

Inspiration.

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