## power series solutions

Hi, I have an exam on differential equation soon, so i was wondering if someone can help me with the power series methods, ordinary points and frobenius.

Like, after you've generated the series, like for example, $a_0 = 1, a_1 = 2x etc$

is there an easy way to find the relationship in terms of a sum, that can be applied to all questions.?

Like all i know is:
to generate even coefficients in the denominator multiply by:
$\frac{1}{(2n)!}$

to generate odd coefficients in the denominator multiply by:
$\frac{1}{(2n+1)!}$

So are there any more tricks that could help me? or is that it??
thank you