Maximum value or bounds of a sequence based on its Z tranform

Question

Consider a sequence $\{a_i\}_{i=0}^{\infty}$ of real numbers and its Z tranform $$A(z)=\sum_{i=0}^{\infty}a_iz^{-i}$$ We assume that all poles of $A(z)$ lie in the interior of the unit circle. Thus, the inverse Z transform is defined by $$a_i=\frac{1}{2\pi i}\oint{A(z)z^{i-1}dz}$$ where the contour of integration is the unit circle. I was wandering if it is possible to identify the $\sup_{0\leq i< \infty}|a_i|$ or some suitable bound based on the values of $A(z)$.