  It is a standard result that the Hankel determinants for a sequence stay
invariant after performing the binomial transform on this sequence. In this
work, we extend the scenario to $q$-binomial transforms and study the behavior
of the leading coefficient in such Hankel determinants. We also investigate the
leading coefficient in the Hankel determinants for even-indexed Bernoulli
polynomials with recourse to a curious binomial transform. In particular, the
degrees of these Hankel determinants share the same nature as those in one of
the $q$-binomial cases.
