Suppose $\displaystyle f(x)=\sum_{n=0}^{\infty}a_nx^n$ satisfies the equation $\displaystyle f(x)\ln(f(x))=x.$ Find a closed-form expression for $\displaystyle a_n, \ n \geq 0.$

Note: Don't worry about details such as where $\displaystyle x$ and $\displaystyle f(x)$ are defined, etc. You may assume whatever is needed! (Smile)