The given equation is x(x-1)y'' + 3y' - 2y = 0.
I was able to discern that a(k+1) = a(k) * [(k+r)(k+r-1)-2]/[(k+r+1)(k+r-3)], and the roots are 0 and 4. That recursive equation gives me the correct coefficients for a(0) through a(3), and of course, a(4) is undefined. But I can't get it right from a(5) on. I used the root 0 to get those first few a's; was I supposed to switch over to 4?