\[\Large{\frac{a_n}{a_{n-1}} = \sqrt[6]{\frac{a_{n-1}}{a^2_{n-2}}}}\]

Define a sequence \(a_n\) that satisfies the recurrence relation as described above where \(n \geq 2 , a_0 = e , a_1 = e^2\).

Find the value of \(\displaystyle\large{ \lim_{n \to \infty} a_n}\).

**Bonus**: Generalize for \(a_n\).

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