  In the context of $\mathcal{N}=4$ SYM, we compute the finite 't Hooft
coupling $\lambda$ correction to the non-linear second-order hydrodynamic
coefficient $\lambda_3$ from a Kubo formula based on fully retarded three-point
functions using AdS/CFT. Although $\lambda_3$ is known to vanish in the
infinite 't Hooft coupling limit, we find that the finite $\lambda$ correction
is non-zero. We also present a set of Kubo formulae for the non-linear
coefficients $\lambda_{1,2,3}$, which is more convenient than the one that has
appeared recently elsewhere.
