  Recently, there has been renewed interest in studying the asymptotic
properties of the number theoretic partition function $p(n)$. Ramanujan, Hardy,
and Rademacher provided detailed asymptotic analyses for $p(n)$. Presently,
attention has shifted towards Poincar\'e-type asymptotic expansions,
characterised by their simplicity albeit reduced accuracy compared to the
earlier works of Ramanujan, Hardy, and Rademacher. This paper aims to establish
computable error bounds for one such simplified expansion. The bounds presented
herein are sharper, and their derivation is considerably simpler compared to
those found in recent literature.
