Are derivative indices summed in indicial notation?

A paper I'm reading uses indicial notation and the convention that $u_{j,k}$ means the derivative with respect to $x_k$. Which one of these interpretations are correct?

$$A_{ijk}u_{j,k} = \sum_{j}A_{ijk} \frac{\delta u_j}{\delta x_k}$$

$$A_{ijk}u_{j,k} = \sum_{j,k}A_{ijk} \frac{\delta u_j}{\delta x_k}$$