Specific contour integral around essential singularity

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Is there a "closed-form" expression for $$ \oint \mathrm{d}z \, \exp\left( a z^2 + b z + c/z \right) \,, $$ for $a,b,c \in \mathbb{C}$, where $\oint$ means contour integral along a path winding once (counterclockwise) around the origin $z = 0$?