Is there a nice description of the field of fractions of the ring of polynomials with integer coefficients?

Is there a nice description of the field of fractions of the ring of
polynomials with integer coefficients?

Let $\mathbb{Z}[x]$ denote the ring of polynomials (in the formal variable
$x$) with integer coefficients. Since $\mathbb{Z}[x]$ is an integral
domain, we can form its field of quotients, call it $Q.$
Is there a nice description of $Q$? I don't think $Q = \mathbb{Q}((x)),$
or in other words I don't think $Q = $ the set of all formal Laurent
polynomials with rational coefficients, because for example I think that
$$\sum_{n=0}^\infty \frac{x^n}{n!} \notin Q.$$