I am trying to invert (?) a power series. Let $$y(x) = \sum_{k \geq 1} a_k x^k$$ I need to find the coefficients $b_k$ such that $$x(y) = \sum_{k \geq 1} b_k y^k$$
For example, I have the following power series (assuming convergence) $$x(z) = \sum_{k \geq 1} \frac{z^k}{k^n} \hspace{1cm} \text{n > 0}$$ and I want z(x)