Brent

I haven't been able to track down the kid's actual solution yet, so all I have to go on is what you've said. The method you described would be the power series method or Forbenius method, which is used all over the place for things like orthogonal polynomials (Legendre polynomials, Laguerre polynomials, Bessel functions, etc.). Is there something more to his solution? Could you please provide a link to his work?