n!=∑i=0n(−1)n−i(in)in=∑i=0n[in]n!=\sum_{i=0}^n(-1)^{n-i}(_i^n)i^n=\sum_{i=0}^n[_i^n]n!=∑i=0n(−1)n−i(in)in=∑i=0n[in]
