Consider a real-valued sequence $(a_0,a_1,a_2,....)$ and the "$n$-stretch"-transformation, which inserts $n$ zeros between each element, for example $n=2$ would represent the transformation
$$(a_0,a_1,a_2,...)\mapsto(a_0,0,0,a_1,0,0,a_2,0,0,...).$$
Now, considering the sequence's generating function $$G(x)=a_0+a_1 x+a_2 x^2+...,$$ obviously, the $n$-stretch is represented by $$G(x)\mapsto G(x^{n+1}).$$
Now I wonder if for the exponential generating function
$$E(x)=a_0 + a_1\frac{x^1}{1!} + a_2\frac{x^2}{2!}+...,$$
there exists also such a simple representation
$$E(x)\mapsto?$$