  In a reinforced Galton-Watson process with reproduction law
$\boldsymbol{\nu}$ and memory parameter $q\in(0,1)$, the number of children of
a typical individual either, with probability $q$, repeats that of one of its
forebears picked uniformly at random, or, with complementary probability $1-q$,
is given by an independent sample from $\boldsymbol{\nu}$. We estimate the
average size of the population at a large generation, and in particular, we
determine explicitly the Malthusian growth rate in terms of $\boldsymbol{\nu}$
and $q$. Our approach via the analysis of transport equations owns much to
works by Flajolet and co-authors.
