Suppose that i have a power series defined by $$\begin{align} f(z)&=\sum_{n=0}^{+\infty}a_nz^n\\ a_0&=0\\ a_1&=1\\ a_n&=\frac{a_{n-1}+a_{n-2}+a_{n-1}a_{n-2}}{3} \end{align}$$ How i can find the convergence radius of $f$
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I think the series converges for $|z|<1$. – Mhenni Benghorbal Jan 15 '15 at 01:44