  We study a polynomial sequence $C_n(x|q)$ defined as a solution of a
$q$-difference equation. This sequence, evaluated at $q$-integers, interpolates
Carlitz-Riordan's $q$-ballot numbers. In the basis given by some kind of
$q$-binomial coefficients, the coefficients are again some $q$-ballot numbers.
We obtain in a combinatorial way another curious recurrence relation for these
polynomials.
