Given the recurrence relation: a_{n}=2a_{n-1}+2^{n} with a_{0}=1
and given the functional equation: g(x) - 1 = 2x * g(x) + 2x/(1-2x) for the recurrence relation, solve the recurrence relation using generating functions.
I brought the 1 over, since it is the initial condition to obtain g(x) = 1 + 2x * g(x) + 2x/(1-2x)
I don't know where to proceed? Will I need to use partial fractions? I need a refresher D: