Fubini
A131689 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ k! \ {n \brace k} } \)
\(T_{n, n - k}\) ➤ Trev ➤ 1 1 0 2 1 0 6 6 1 0 24 36 14 1 0 120
\((T_{n + 1, n - k + 1})^{-1}\) ➤ Tinvrev11 ➤ 1 -2 1 6 -6 1 -36 48 -14 1 540 -780 270
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 0 1 3 0 1 7 13 0 1 15 51 75 0 1
\(T_{n + 1, k + 1}\ (k + 1) \) ➤ Tder ➤ 1 1 4 1 12 18 1 28 108 96 1 60 450 960
\(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 2 6 504 1200 4352400 6501600
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 1 0 6 1 0 36 14 1 0 240 150 30 1 0
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 0 0 1 0 1 6 0 1 14 36 0 1 30 150 240 0
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 2 0 6 1 24 6 0 120 36 1 720 240 14
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 2 3 3 6 12 13 13 24 60 74 75 75
\(T_{n, n-k}\ (-1)^{n-k}\) ➤ RevTalt ➤ 1 1 0 2 -1 0 6 -6 1 0 24 -36 14 -1 0
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 1 0 6 2 0 36 28 3 0 240 300 90 4 0
\(\sum_{k=0}^{n} T_{n, n-k}\ (1 - [2 | k])\) ➤ RevOddSum ➤ 0 0 1 6 37 270 2341 23646 272917
\(\sum_{k=0}^{n/2} T_{n - k, n-k}\) ➤ RevAntiDSum ➤ 1 1 2 7 30 157 974 6991 57030 521341
\(T_{n, n / 2}\) ➤ RevColMiddle ➤ 1 1 1 6 14 150 540 8400 40824 834120
\(\sum_{k=0}^{n} T_{n, n-k}\ k\) ➤ RevTransNat0 ➤ 0 0 1 8 67 634 6793 81780 1095967
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 0 1 10 101 1126 13917 190002 2848477