What you have is correct. You have forgotten that because there will only be even powers of x, the terms with the odd powers of x have 0 coefficient.
I have another function wich I have to represent as as a power series
it seems to me that I got something different because the coefficients I get are not correct.
what I got is with a Radius of convergence R= 1/5
the first few coefficients I get are
I know that my radius of convergence is correct, but I can't understand where is my mistake with the coefficients,