Rencontres
A008290 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ \binom{n}{k} derangements(n - k) } \)
\(T^{-1}_{n, n - k}\) ➤ Trevinv ➤ 1 1 0 1 0 -1 1 0 -3 -2 1 0 -6 -8 -3 1 0
\(T_{n + 1, k + 1} \) ➤ Toff11 ➤ 1 0 1 3 0 1 8 6 0 1 45 20 10 0 1 264
\(T_{n + 1, n - k + 1} \) ➤ Trev11 ➤ 1 1 0 1 0 3 1 0 6 8 1 0 10 20 45 1 0 15
\(T^{-1}_{n + 1, k + 1}\) ➤ Tinv11 ➤ 1 0 1 -3 0 1 -8 -6 0 1 -15 -20 -10 0 1
\(T^{-1}_{n + 1, n - k + 1}\) ➤ Trevinv11 ➤ 1 1 0 1 0 -3 1 0 -6 -8 1 0 -10 -20 -15
\(T_{n - k, k} \ \ (k \le n/2)\) ➤ Tantidiag ➤ 1 0 1 1 2 0 9 3 1 44 8 0 265 45 6 1
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 1 1 2 2 5 5 6 9 17 23 23 24 44 89
\(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 1 6 72 1980 629640 75661740
\(\sum_{k=0}^{n/2} T_{n - k, k}\) ➤ AntiDSum ➤ 1 0 2 2 13 52 317 2138 16834 149292
\(T_{n, n / 2}\) ➤ ColMiddle ➤ 1 0 0 3 6 20 40 315 630 5544 11088
\(T_{2 n + 1, n}\) ➤ CentralO ➤ 0 3 20 315 5544 122430 3181464 95450355
\(\sum_{k=0}^{n} T_{n, k} \ \binom{n}{k} \) ➤ BinConv ➤ 1 1 2 12 78 570 4900 48160 530390
\(\sum_{k=0}^{n} T_{n, k} \ (-1)^{n - k} \ \binom{n}{k} \) ➤ InvBinConv ➤ 1 1 2 8 14 82 132 744 4566 -33442
\(\sum_{k=0}^{3} T_{3, k}\ n^k\) ➤ PolyRow3 ➤ 2 6 16 38 78 142 236 366 538 758 1032
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 0 1 0 3 2 0 6 8 9 0 10 20 45 44 0 15
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 0 1 0 2 3 0 9 8 6 0 44 45 20 10 0 265
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 1 1 2 1 1 4 6 1 1 7 15 24 1 1 11
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 0 2 0 6 6 0 12 24 36 0 20 60 180 220
\(\sum_{k=0}^{n} T_{n, n-k}\ [2 | k]\) ➤ RevEvenSum ➤ 1 1 2 4 16 56 416 2192 22912 156928
\(\sum_{k=0}^{n} T_{n, n-k}\ (1 - [2 | k])\) ➤ RevOddSum ➤ 0 0 0 2 8 64 304 2848 17408 205952
\(T_{n, n / 2}\) ➤ RevColMiddle ➤ 1 1 0 0 6 10 40 70 630 1134 11088 20328
\(T_{2 n + 1, n}\) ➤ RevCentralO ➤ 1 0 10 70 1134 20328 454740 11930490
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 0 4 30 240 2040 18720 186480 2016000
\(\sum_{k=0}^{3} T_{3, n-k}\ n^k\) ➤ RevPolyRow3 ➤ 1 6 29 82 177 326 541 834 1217 1702
\(\sum_{k=0}^{n} T_{n, n-k}\ 3^k\) ➤ RevPolyCol3 ➤ 1 1 10 82 1000 14968 269488 5659120
\(\sum_{k=0}^{n} T_{n, n-k}\ n^k\) ➤ RevPolyDiag ➤ 1 1 5 82 2913 168376 14600845