  Let $b \ge 2$ and $\ell \ge 1$ be integers. We establish that there is an
absolute real number $K$ such that all the partial quotients of the rational
number $$ \prod_{h = 0}^\ell \, (1 - b^{-2^h}), $$ of denominator
$b^{2^{\ell+1} - 1}$, do not exceed $\exp(K (\log b)^2 \sqrt{\ell}
2^{\ell/2})$.
