This is a problem from the book Discrete-Time Speech Signal Processing by Thomas Quatieri, Chapter 6 Problem 13:
Suppose $h[n]$ is all-pole (minimum-phase) of order $p$. Show that the all-pole (predictor) coefficients can be obtained recursively from the first $p$ complex cepstral coefficients of $h[n]$.
I was only able to solve for the opposite. i.e. complex cepstral coefficients from the pole coefficients.