  An $n$-sesquicategory is an $n$-globular set with strictly associative and
unital composition and whiskering operations, which are however not required to
satisfy the Godement interchange laws which hold in $n$-categories. In
arXiv:2202.09293 we showed how these can be defined as algebras over a monad
$T_n^{D^s}$ whose operations are simple string diagrams. In this paper, we give
an explicit description of computads for the monad $T_n^{D^s}$ and we prove
that the category of computads for this monad is a presheaf category. We use
this to describe a string diagram notation for representing arbitrary
composites in $n$-sesquicategories. This is a step towards a theory of string
diagrams for semistrict $n$-categories.
