**Reopened** The author of [Generating function of the number of permutations of length n with exactly k fixed points](https://math.stackexchange.com/questions/4216110/generating-function-of-the-number-of-permutations-of-length-n-with-exactly-k-fix) has added the source of the question and the solution for half of the question. I think that the question has an interesting answer and I would like to post it. I would like to see this question reopened.