TITLE: Partial fraction of $\frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$
QUESTION [9 upvotes]: How should you break $\displaystyle \frac{x^n}{(1-x)(1-2x)(1-3x)\ldots(1-nx)}$ into partial fractions?

REPLY [4 votes]: It is worth emphasizing that both of the presented solutions essentially employ what is known as Heaviside's cover-up method. As I explained in this answer, this method works generally, i.e. even for nonlinear denominators. As should be evident from the presentation that I gave there, the solution can be constructed by a purely algebraic deterministic algorithm, i.e. without employing any analytic techniques (residue calculus, limits, L'Hopital's rule, etc). Moreover, this is frequently the most efficient way to proceed - even for manual calculations.