Let $\D$ be the Lie algebra of regular differentialoperators on ${ \C} \setminus \{ 0\}$, and ${ \hD}= { \D} + { \C} C$ be the central extension of ${ \D}$. Let $W_{ 1+\infty,-N}$ be the vertex algebra associated to the irreducible vacuum $\hD$-module with the central charge $c=-N$. We show that $W_{ 1+\infty,-N}$ is a subalgebra of the Heisenberg vertex algebra M(1) with $2 N$ generators, and construct 2N-dimensional family of irreducible $W_{ 1+\infty,-N}$-modules. Considering these modules as $\hD$-modules, we identify the corresponding highest weights.

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Representations of the vertex algebra $W_{1+\infty}$ with a negative integer central charge