Chebyshevs
A049310 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ is(n+k \text{ even}) ? \binom{(n+k)/2}{k} : 0 } \)
\(T_{n + 1, n - k + 1} \) ➤ Trev11 ➤ 1 1 0 1 0 -2 1 0 -3 0 1 0 -4 0 3 1 0 -5
\(T^{-1}_{n + 1, n - k + 1}\) ➤ Trevinv11 ➤ 1 1 0 1 0 2 1 0 3 0 1 0 4 0 5 1 0 5 0 9
\(T_{n - k, k} \ \ (k \le n/2)\) ➤ Tantidiag ➤ 1 0 -1 1 0 0 1 -2 1 0 0 0 -1 3 -3 1 0 0
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 -1 -1 0 0 -2 -2 -1 1 1 -2 -2 -1 0
\(\text{gcd}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablGcd ➤ 1 1 1 2 3 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, j}\) ➤ AccSum ➤ 1 1 -2 -5 -3 4 9 5 -6 -13 -7 8 17 9 -10
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, n - j}\) ➤ AccRevSum ➤ 1 2 2 0 -3 -4 -1 4 6 2 -5 -8 -3 6 10 4
\(T_{n, n / 2}\) ➤ ColMiddle ➤ 1 0 0 -2 -3 0 0 10 15 0 0 -56 -84 0 0
\(\sum_{k=0}^{n} T_{n, k} \ (k + 1)\) ➤ TransNat1 ➤ 1 2 2 0 -3 -4 -1 4 6 2 -5 -8 -3 6 10 4
\(\sum_{k=0}^{n} T_{n, k} \ k^{2}\) ➤ TransSqrs ➤ 0 1 4 7 4 -8 -20 -15 12 39 32 -16 -64
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 0 -1 0 -2 0 0 -3 0 1 0 -4 0 3 0 0 -5
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 0 -1 0 0 -2 0 1 0 -3 0 0 3 0 -4 0 -1 0
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 1 1 0 1 1 -1 -1 1 1 -2 -2 -1 1 1
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 0 -2 0 -4 0 0 -6 0 4 0 -8 0 12 0 0
\(\sum_{k=0}^{n} \sum_{j=0}^{k} T_{n, n - j}\) ➤ RevAccRevSum ➤ 1 1 -2 -5 -3 4 9 5 -6 -13 -7 8 17 9 -10
\(T_{n, n / 2}\) ➤ RevColMiddle ➤ 1 1 0 0 -3 -4 0 0 15 21 0 0 -84 -120 0
\(\sum_{k=0}^{n} T_{n, n-k}\ k\) ➤ RevTransNat0 ➤ 0 0 -2 -4 -2 4 8 4 -6 -12 -6 8 16 8 -10
\(\sum_{k=0}^{n} T_{n, n-k}\ (k + 1)\) ➤ RevTransNat1 ➤ 1 1 -2 -5 -3 4 9 5 -6 -13 -7 8 17 9 -10
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 0 -4 -8 4 32 40 -8 -84 -96 12 160 176
\(\sum_{k=0}^{n} T_{n, n-k}\ n^k\) ➤ RevPolyDiag ➤ 1 1 -3 -17 209 1776 -39059 -446879