Delannoy
A008288 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ \text{Hyper}([-k, k - n], [1], 2) } \)
\(T_{n + 1, k + 1} \) ➤ Toff11 ➤ 1 3 1 5 5 1 7 13 7 1 9 25 25 9 1 11 41
\(T_{n + 1, n - k + 1} \) ➤ Trev11 ➤ 1 1 3 1 5 5 1 7 13 7 1 9 25 25 9 1 11
\(T^{-1}_{n + 1, k + 1}\) ➤ Tinv11 ➤ 1 -3 1 10 -5 1 -38 22 -7 1 158 -98 38
\(T^{-1}_{n + 1, n - k + 1}\) ➤ Trevinv11 ➤ 1 1 -3 1 -5 10 1 -7 22 -38 1 -9 38 -98
\(T_{n - k, k} \ \ (k \le n/2)\) ➤ Tantidiag ➤ 1 1 1 1 1 3 1 5 1 1 7 5 1 9 13 1 1 11
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 1 2 1 4 5 1 6 11 12 1 8 21 28 29 1 10
\(T_{n + 1, k + 1}\ (k + 1) \) ➤ Tder ➤ 1 3 2 5 10 3 7 26 21 4 9 50 75 36 5 11
\(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 3 5 91 225 28413 102297 2100945
\(\sum_{k=0}^{n} T_{n, k}\ (1 - [2 | k])\) ➤ OddSum ➤ 0 1 3 6 14 35 85 204 492 1189 2871 6930
\(\sum_{k=0}^{n} T_{n, k} \ k^{2}\) ➤ TransSqrs ➤ 0 1 7 34 138 503 1709 5524 17204 52061
\(\sum_{k=0}^{3} T_{3, k}\ n^k\) ➤ PolyRow3 ➤ 1 12 39 88 165 276 427 624 873 1180
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 1 3 1 5 5 1 7 13 7 1 9 25 25 9 1 11 41
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 1 1 3 1 5 5 1 7 13 7 1 9 25 25 9 1 11
\(T^{-1}_{n + 1, n-k}\) ➤ RevTinv11 ➤ 1 -3 1 10 -5 1 -38 22 -7 1 158 -98 38
\(T^{-1}_{n + 1, n-k}\) ➤ RevTrevinv11 ➤ 1 1 -3 1 -5 10 1 -7 22 -38 1 -9 38 -98
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 1 1 1 3 1 5 1 1 7 5 1 9 13 1 1 11
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 2 1 4 5 1 6 11 12 1 8 21 28 29 1 10
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 1 3 2 5 10 3 7 26 21 4 9 50 75 36 5 11
\(\sum_{k=0}^{n} T_{n, n-k}\ (1 - [2 | k])\) ➤ RevOddSum ➤ 0 1 3 6 14 35 85 204 492 1189 2871 6930
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 1 7 34 138 503 1709 5524 17204 52061
\(\sum_{k=0}^{3} T_{3, n-k}\ n^k\) ➤ RevPolyRow3 ➤ 1 12 39 88 165 276 427 624 873 1180