  In this note, we provide a non trivial example of differential equation
driven by a fractional Brownian motion with Hurst parameter 1/3 < H < 1/2,
whose solution admits a smooth density with respect to Lebesgue's measure. The
result is obtained through the use of an explicit representation of the
solution when the vector fields of the equation are nilpotent, plus a Norris
type lemma in the rough paths context.
