Frobenius & Special Functions · Hard problem

The equation $2x^2y'' + 3xy' - (1 + x)y = 0$ has a regular singular point at $x = 0$. Let $y = \sum_{n\ge0}a_nx^{n+r}$ be the Frobenius solution for the larger indicial root, with $a_0 = 1$. Compute $a_3$. Express your answer as a common fraction.