  We consider D-finite power series $f(z)=\sum a_n z^n$ with coefficients in a
number field $K$. We show that there is a dichotomy governing the behaviour of
$h(a_n)$ as a function of $n$, where $h$ is the absolute logarithmic Weil
height. As an immediate consequence of our results, we have that either $f(z)$
is rational or $h(a_n)>[K:\mathbb{Q}]^{-1}\cdot \log(n)+O(1)$ for $n$ in a set
of positive upper density and this is best possible when $K=\mathbb{Q}$.
