Orderedcycle
A225479 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ k! {n \brack k} } \)
\(T_{n, n - k}\) ➤ Trev ➤ 1 1 0 2 1 0 6 6 2 0 24 36 22 6 0 120
\(T_{n - k, k} \ \ (k \le n/2)\) ➤ Tantidiag ➤ 1 0 0 1 0 1 0 2 2 0 6 6 0 24 22 6 0 120
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 0 1 3 0 2 8 14 0 6 28 64 88 0 24
\(T_{n + 1, k + 1}\ (k + 1) \) ➤ Tder ➤ 1 1 4 2 12 18 6 44 108 96 24 200 630
\(T_{n + 2, n}\) ➤ TablDiag2 ➤ 0 2 22 210 2040 21000 231840 2751840
\(T_{n + 3, n}\) ➤ TablDiag3 ➤ 0 6 100 1350 17640 235200 3265920
\(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 2 6 792 8400 25153200 76734000
\(\sum_{k=0}^{n} T_{n, k}\ (1 - [2 | k])\) ➤ OddSum ➤ 0 1 1 8 42 354 3270 36504 460152
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, j}\) ➤ AccSum ➤ 1 1 4 24 186 1750 19300 243768 3467184
\(T_{2 n + 1, n}\) ➤ CentralO ➤ 0 2 100 9744 1614816 410031600
\(\sum_{k=0}^{n} T_{n, k} \ k^{2}\) ➤ TransSqrs ➤ 0 1 9 80 802 9154 118022 1701048
\(\sum_{k=0}^{3} T_{3, k}\ n^k\) ➤ PolyRow3 ➤ 0 14 76 222 488 910 1524 2366 3472 4878
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 1 0 6 2 0 36 22 6 0 240 210 100 24 0
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 0 0 1 0 2 6 0 6 22 36 0 24 100 210 240
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 2 0 6 1 24 6 0 120 36 2 720 240 22
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 2 3 3 6 12 14 14 24 60 82 88 88
\(T_{n, n-k}\ (-1)^{n-k}\) ➤ RevTalt ➤ 1 1 0 2 -1 0 6 -6 2 0 24 -36 22 -6 0
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 1 0 6 4 0 36 44 18 0 240 420 300 96 0
\(\sum_{k=0}^{n} T_{n, n-k}\ [2 | k]\) ➤ RevEvenSum ➤ 1 1 2 8 46 354 3308 36504 460752
\(\sum_{k=0}^{n} T_{n, n-k}\ (1 - [2 | k])\) ➤ RevOddSum ➤ 0 0 1 6 42 340 3270 36288 460152
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, n - j}\) ➤ RevAccRevSum ➤ 1 1 4 24 186 1750 19300 243768 3467184
\(\sum_{k=0}^{n/2} T_{n - k, n-k}\) ➤ RevAntiDSum ➤ 1 1 2 7 30 158 982 7056 57580 526374
\(T_{n, n / 2}\) ➤ RevColMiddle ➤ 1 1 1 6 22 210 1350 17640 162456
\(\sum_{k=0}^{n} T_{n, n-k}\ k\) ➤ RevTransNat0 ➤ 0 0 1 10 98 1056 12722 170976 2546280
\(\sum_{k=0}^{n} T_{n, n-k}\ (k + 1)\) ➤ RevTransNat1 ➤ 1 1 4 24 186 1750 19300 243768 3467184
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 0 1 14 178 2364 33878 527904 8942232