  In this paper we study the following family of hypergeometric polynomials:
$y_n(x) = \frac{ (-1)^\rho }{ n! } x^n {}_2 F_0(-n,\rho;-;-\frac{1}{x})$,
depending on a parameter $\rho\in\mathbb{N}$. Differential equations of orders
$\rho+1$ and $2$ for these polynomials are given. A recurrence relation for
$y_n$ is derived as well. Polynomials $y_n$ are Sobolev orthogonal polynomials
on the unit circle with an explicit matrix measure.
