Fallingfact
A008279 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ n! / (n - k)! } \)
\(T_{n + 1, n - k + 1} \) ➤ Trev11 ➤ 1 2 2 6 6 3 24 24 12 4 120 120 60 20 5
\(T_{n + 1, k + 1}\ (k + 1) \) ➤ Tder ➤ 1 2 4 3 12 18 4 24 72 96 5 40 180 480
\(\sum_{k=0}^{3} T_{3, k}\ n^k\) ➤ PolyRow3 ➤ 1 16 79 226 493 916 1531 2374 3481 4888
\(T^{-1}_{n + 1, n-k}\) ➤ RevTinv11 ➤ 1 -2 1 0 -3 1 0 0 -4 1 0 0 0 -5 1 0 0 0
\(T^{-1}_{n + 1, n-k}\) ➤ RevTrevinv11 ➤ 1 1 -2 1 -3 0 1 -4 0 0 1 -5 0 0 0 1 -6
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 2 1 6 2 24 6 1 120 24 3 720 120 12
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 1 2 2 6 6 3 24 24 12 4 120 120 60 20 5
\(\sum_{k=0}^{3} T_{3, n-k}\ n^k\) ➤ RevPolyRow3 ➤ 6 16 38 78 142 236 366 538 758 1032