Limits are easy... right?

Calculus Level 3

The limit \[\lim_{n\to\infty}\frac1n\left(\prod^n_{k=1}\Gamma\left(\frac1k\right)\right)^{1/n}\]

Can be written as \[a\,e^{b}+c\]

Find the value of \(|a|+|b|+|c|\).


Details and Assumptions - \(e\) denotes the base of the natural logarithm.

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