Divisibility
A113704 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ [n=0 \text{ or } k \text{ divides } n] } \)
\(T_{n, n - k}\) ➤ Trev ➤ 1 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1
\(T_{n - k, k} \ \ (k \le n/2)\) ➤ Tantidiag ➤ 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 0 1 2 0 1 1 2 0 1 2 2 3 0 1 1 1 1
\(\sum_{k=0}^{n} T_{n, k} \ (-2)^{n - k} \) ➤ NegHalf ➤ 1 1 -1 5 -3 17 -23 65 -47 321 -287 1025
\(\sum_{k=0}^{n} T_{n, k} \ (-1)^{n - k} \ \binom{n}{k} \) ➤ InvBinConv ➤ 1 1 -1 4 3 6 -10 8 91 94 -216 12 1254
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 1 2 2 1 1 2 2 1 1 2 3 3 1 1 1 1 2
\(T_{n, n-k}\ (-1)^{n-k}\) ➤ RevTalt ➤ 1 1 0 1 -1 0 1 0 1 0 1 0 1 -1 0 1 0 0 0
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 1 0 0 2 0 0 2 3 0 0 0 0 4 0 0 0 3 4 5
\(\sum_{k=0}^{n} T_{n, n-k}\ (-2)^{n - k} \) ➤ RevNegHalf ➤ 1 -2 2 -10 18 -34 58 -130 274 -522 994
\(\sum_{k=0}^{n} T_{n, n-k}\ n^k\) ➤ RevPolyDiag ➤ 1 1 3 10 81 626 9289 117650 2363393