  In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a
sequence of polynomials $S_n(q)$ as given by
$$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$$
and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By
imitating a result of Liu and Wang on generating new $q$-log-convex sequences
of polynomials from old ones, we obtain a sufficient condition for determining
the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion,
we then give an affirmative answer to Sun's conjecture.
