Falling and Rising Factorials m2=mn=m(m-1)m-2)(m-n+1）=m-m m! m元=mm=m(m+1)(m+2）)…(m+n-1) n!=n2=1n m n n! Hengfeng Wei (hfweixinju.edu.cn) 2-3 Counting March12,20207/34Falling and Rising Factorials mn = (m)n = m(m − 1)(m − 2)· · ·(m − n + 1) = m! (m − n)! mn¯ = m(n) = m(m + 1)(m + 2)· · ·(m + n − 1) n! = n n = 1n¯ m n ! = mn n! Hengfeng Wei (hfwei@nju.edu.cn) 2-3 Counting March 12, 2020 7 / 34