Frobenius & Special Functions · Easy problem

For $xy'' + 3y' + y = 0$, the Frobenius series $y = \sum_{n\ge0}a_nx^{n}$ for the indicial root $r = 0$ satisfies $n(n+2)\,a_n = -a_{n-1}$ for $n \ge 1$. With $a_0 = 1$, compute $a_3$. Express your answer as a common fraction.