  Power-law interactions play a key role in a large variety of physical
systems. In the presence of disorder, these systems may undergo many-body
localization for a sufficiently large disorder. Within the many-body localized
phase the system presents in time an algebraic growth of entanglement entropy,
$S_{vN}(t)\propto t^{\gamma}$. Whereas the critical disorder for many-body
localization depends on the system parameters, we find by extensive numerical
calculations that the exponent $\gamma$ acquires a universal value
$\gamma_c\simeq 0.33$ at the many-body localization transition, for different
lattice models and decay powers. Moreover, our results suggest an intriguing
relation between $\gamma_c$ and the critical minimal decay power of
interactions necessary for the observation of many-body localization.
