L'Hopital is Invalid!

$\large\ \lim _{ n\rightarrow \infty }{ \frac { e{ \left( 1 - \frac { 1 }{ n } \right) }^{ n } - 1 }{ { n }^{ \alpha } } }$

If the limit above exists and is equal to a non-zero constant $c$ , then find the value of $12(c - \alpha)$ .