Reopened
Three days ago, Asymptotic expansion of $\sum_{k=1}^n {n \choose k} (-1)^k \frac 1 {1-x^k} $ received three close votes due to lack of context. Since then, the author added clarification and context. Yesterday, there were two close votes arising from a review, and those closed the question. However, I think that this poster has shown a decent effort to improve their post.
The question is interesting and I request that this question be reopened.
I apologize that I forgot to mention that I have answered this question.