Laguerre
A021009 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ \binom{n}{k}\, \frac{n!}{k!} } \)
\(T_{n + 1, k + 1} \) ➤ Toff11 ➤ 1 4 1 18 9 1 96 72 16 1 600 600 200 25
\(T_{n + 1, n - k + 1} \) ➤ Trev11 ➤ 1 1 4 1 9 18 1 16 72 96 1 25 200 600
\(T^{-1}_{n + 1, k + 1}\) ➤ Tinv11 ➤ 1 -4 1 18 -9 1 -96 72 -16 1 600 -600
\(T^{-1}_{n + 1, n - k + 1}\) ➤ Trevinv11 ➤ 1 1 -4 1 -9 18 1 -16 72 -96 1 -25 200
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 1 2 2 6 7 6 24 33 34 24 120 192 208
\(T_{n + 1, k + 1}\ (k + 1) \) ➤ Tder ➤ 1 4 2 18 18 3 96 144 48 4 600 1200 600
\(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 4 18 288 600 21600 529200 11289600
\(\text{max}_{k=0}^{n}\ | T_{n, k} |\) ➤ TablMax ➤ 1 1 4 18 96 600 5400 52920 564480
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, j}\) ➤ AccSum ➤ 1 3 15 97 753 6771 68983 783945 9820737
\(T_{2 n + 1, n}\) ➤ CentralO ➤ 1 18 600 29400 1905120 153679680
\(\sum_{k=0}^{3} T_{3, k}\ n^k\) ➤ PolyRow3 ➤ 6 34 86 168 286 446 654 916 1238 1626
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 1 4 2 9 18 6 16 72 96 24 25 200 600 600
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 1 2 4 6 18 9 24 96 72 16 120 600 600
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 1 1 1 4 1 9 2 1 16 18 1 25 72 6 1
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 2 1 5 7 1 10 28 34 1 17 89 185 209
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 1 4 4 9 36 18 16 144 288 96 25 400 1800
\(\sum_{k=0}^{n} T_{n, n-k}\ [2 | k]\) ➤ RevEvenSum ➤ 1 1 3 19 97 801 6571 65563 723969
\(\sum_{k=0}^{n} T_{n, n-k}\ (1 - [2 | k])\) ➤ RevOddSum ➤ 0 1 4 15 112 745 6756 65359 717760
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, n - j}\) ➤ RevAccRevSum ➤ 1 3 15 97 753 6771 68983 783945 9820737
\(\sum_{k=0}^{n/2} T_{n - k, n-k}\) ➤ RevAntiDSum ➤ 1 1 2 5 12 35 104 333 1124 3947 14520
\(T_{n, n / 2}\) ➤ RevColMiddle ➤ 1 1 4 9 72 200 2400 7350 117600 381024
\(T_{2 n + 1, n}\) ➤ RevCentralO ➤ 1 9 200 7350 381024 25613280 2120152320
\(\sum_{k=0}^{n} T_{n, n-k}\ (k + 1)\) ➤ RevTransNat1 ➤ 1 3 15 97 753 6771 68983 783945 9820737
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 1 12 135 1552 18825 243756 3380167
\(\sum_{k=0}^{3} T_{3, n-k}\ n^k\) ➤ RevPolyRow3 ➤ 1 34 139 352 709 1246 1999 3004 4297