I wanted to know if there was and solution to the following equation.
$\left(N-n+1\right)E_{n+2} - NE_{n+1} + \left(n+1\right)E_{n} + N = 0$
Where $E_0 = 0$ and $E_1 = 2^N - 1$.
$N$ is just a constant.
I know how to do second order difference equations with constant coefficients using the moment generation functions and some basic calculus of residuals (I have only basic knowledge on the topic). But, this is out of my league.