Solution: ​ 由于\[ x^m = \sum_{i=0}^m{~m~\choose i}{~x~\brace i}i! \] ​ 将所求的式子化成这样，挖掘其性质，考虑是否能从儿子转移(或利用以求得信息)。\[ \begin{aligned} S(u) &= \sum_{i=1}^ndis(u,i)^k\\ &= \sum_{i=1}^n\sum_{j=0}^k{dis(u, i)