From *endomorphisms of rank 1* of the full transformation semigroup $[n]^{[n]}$ or *idempotents* in $[n]^{[n]}$, we have
$$c_n:=\sum_{m=1}^n\binom{n}mm^{n-m}.$$

>**QUESTION.** Is it true that $n$ divides  $c_n - 1$?