Series Solutions · Superchallenge problem

The nonlinear equation $y' = y + y^2$ with $y(0) = 1$ has a power-series solution $y = \sum_{n=0}^{\infty} a_n x^n$ (its coefficients can be found one at a time from the equation). Find $\displaystyle\lim_{n \to \infty} a_n(\ln 2)^n$.