I have an equation

$\displaystyle y''-8y'+16y=0$

And I need to find a power series solution for it. I can write this as

$\displaystyle \sum{a_{n+2}(n+2)(n+1)x^n}-8\sum{a_{n+1}(n+1)x^n}+16\sum{a_{n}x^n}=0$

Now, as I understand it, in order to solve this, I need to get rid of one of the a terms (either $\displaystyle a_{n}$ , $\displaystyle a_{n+1}$ or $\displaystyle a_{n+2}$ ), but I don't know how to do this...

Any guidance is greatly appreciated :)