  We call the \emph{$p$-fundamental string} of a complex simple Lie algebra to
the sequence of irreducible representations having highest weights of the form
$k\omega_1+\omega_p$ for $k\geq0$, where $\omega_j$ denotes the $j$-th
fundamental weight of the associated root system. For a classical complex Lie
algebra, we establish a closed explicit formula for the weight multiplicities
of any representation in any $p$-fundamental string.
