What is the sequence represented by the exponential generating function $e^{x^4}$? Problem
For the exponential generating function $e^{x^{4}}$, give a formula in closed form for the sequence $\{a_n:n \geq 0\}$ it represents.
My Attempt
I have that
$$e^{x^{4}}=\sum_{n=0}^{\infty}\frac{(4n)!\,x^{4n}}{n!\,(4n)!},$$
which leads me to believe that $a_n=\frac{(4n)!}{n!}$. However, the series representation is not in the correct form, because it is not of the form $\sum_{n=0}^{\infty}a_n\frac{x^n}{n!}$. Is my answer still correct?

Define:
$$a_n=\frac{1}{(n/4)!},\ \ {\rm for} \ \ n\equiv0\pmod 4\ {\rm or}\  n=0$$
and
$$a_n=0\ \ {\rm otherwise}$$
