  We find and prove a factorization formula for certain Macdonald
Littlewood-Richardson coefficients $c_{\lambda\mu}^{\nu}(q,t)$. Namely, we
consider the case that the Kostka number $K_{\mu, \nu -\lambda}$ is $1$. This
settles a particular case of a more general conjecture of Richard Stanely. This
conjecture proposes that a factorization formula exists whenever the
corresponding regular Littlewood-Richardson coefficient $c^{\nu}_{\lambda \mu}$
is $1$.
