For $n ,p \in N^*$ , $ 1 \le p \le n$, we define $$ R_n^p = \sum_{k=0}^p (p-k)^n(-1)^k C_{n+1}^k $$Show that: $R_n^{n-p+1} =R_n^p$ .
Source: 1996 Romania NMO X p1
Tags: Sum, algebra, binomial coefficients
For $n ,p \in N^*$ , $ 1 \le p \le n$, we define $$ R_n^p = \sum_{k=0}^p (p-k)^n(-1)^k C_{n+1}^k $$Show that: $R_n^{n-p+1} =R_n^p$ .