In this short paper, we derive an integral representation for Euler sums of hyperharmonic numbers. We use results established by other authors to then show that the integral has a closed-form in terms of zeta values and Stirling numbers of the first kind. Specifically, the integral has the form of $$\int_0^\infty \frac{ t^{ m-1}\ln(1-e^{ -t})}{ (1-e^{ -t})^r} \ dt$$ where $m, r \in \mathbb{ N}$, $m > r$ and $r\ge1$.
Categories: math.NT