Find the sum of the series:

$\displaystyle \sum^{\infty}_{n=0} (-1)^n \frac{2^{n+1}x^{6n}}{n!}$

$\displaystyle = \sum^{\infty}_{n=0} \frac{(-2^nx^6)^n}{n!}$

$\displaystyle = e^{-2^nx^6}$

Where am I wrong? Do I need an index shift because of the $\displaystyle 2^{n+1}$ ?