\begin{align*} A \amp = 1 + 4x + 9x^2 + 16x^3 + \cdots\\ \underline{-\qquad xA} \amp \underline{\,\, = 0 + x + 4x^2 + 9x^3 + 16x^4 + \cdots}\\ (1-x)A \amp = 1 + 3x + 5x^2 + 7x^3 + \cdots \end{align*}
in-context