  Many ${\mathcal W}$-(super)algebras which are defined by the generalized
Drinfeld-Sokolov reduction are also known or expected to have coset
realizations. For example, it was conjectured by Ito that the principal
${\mathcal W}$-superalgebra ${\mathcal W}^k(\mathfrak{sl}(n+1|n))$ is
isomorphic to the coset of $V^{l+1}(\mathfrak{gl}_n)$ inside
$V^{l}(\mathfrak{sl}_{n+1}) \otimes {\mathcal E}(n)$ for generic values of $l$.
Here ${\mathcal E}(n)$ denotes the rank $n$ $bc$-system, which carries an
action of $V^1(\mathfrak{gl}_n)$, and $k$ and $l$ are related by $(k + 1) (l +
n + 1) = 1$. This conjecture is known in the case $n=1$, which is somewhat
degenerate, and we shall prove it in the first nontrivial case $n=2$. As a
consequence, we show that the simple quotient ${\mathcal
W}_k(\mathfrak{sl}(3|2))$ is lisse and rational for all positive integers
$l>1$. These are new examples of rational ${\mathcal W}$-superalgebras.
