  In this note we give a numerical expression for the bandwidth $bw(P_{n}^{d})$
of the $d$-product of a path with $n$ edges, $P_{n}^{d}$. We prove that this
bandwidth is given by the sum of certain multinomial coefficients. We also show
that $bw(P_{n}^{d})$ is bounded above and below by the largest coefficient in
the expansion of $(1+x+...+x^{n})^{k}$, with $k\in{d,d+1}$. Moreover, we
compare the asymptotic behavior of $bw(P_{n}^{d})$ with the bandwidth of the
labeling obtained by ordering the vertices of $P_{n}^{d}$ in lexicographic
order.
