Chebyshevs
A049310 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ is(n+k \text{ even}) ? \binom{(n+k)/2}{k} : 0 } \)
A000007 \(T_{n + 1, n}\) ➤ TablDiag1 ➤ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
---------- \(T_{n + 3, n}\) ➤ TablDiag3 ➤ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
---------- \(\sum_{k=0}^{n/2} T_{n - k, k}\) ➤ AntiDSum ➤ 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
---------- \(\sum_{k=0}^{n} T_{n, n-k}\ (1 - [2 | k])\) ➤ RevOddSum ➤ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A000012 \(T_{n , n}\) ➤ TablDiag0 ➤ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
---------- \(\sum_{k=0}^{1} T_{1, n-k}\ n^k\) ➤ RevPolyRow1 ➤ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
A000027 \(T_{n + 2, n}\) ➤ TablDiag2 ➤ -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12
---------- \(\sum_{k=0}^{1} T_{1, k}\ n^k\) ➤ PolyRow1 ➤ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---------- \(\sum_{k=0}^{n} T_{n, k}\ 2^k\) ➤ PolyCol2 ➤ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
---------- \(\sum_{k=0}^{n} T_{n, n-k}\ (-2)^{n - k} \) ➤ RevNegHalf ➤ 1 -2 3 -4 5 -6 7 -8 9 -10 11 -12 13 -14
A000035 \(T_{n , 0}\) ➤ TablCol0 ➤ 1 0 -1 0 1 0 -1 0 1 0 -1 0 1 0 -1 0 1 0
A000045 \(\sum_{k=0}^{n} | T_{n, k} |\) ➤ AbsSum ➤ 1 1 2 3 5 8 13 21 34 55 89 144 233 377
A000217 \(T_{n + 2, 2}\) ➤ TablCol2 ➤ 1 0 -3 0 6 0 -10 0 15 0 -21 0 28 0 -36
A000292 \(T_{n + 3, 3}\) ➤ TablCol3 ➤ 1 0 -4 0 10 0 -20 0 35 0 -56 0 84 0
A001906 \(\sum_{k=0}^{n} T_{n, k}\ 3^k\) ➤ PolyCol3 ➤ 1 3 8 21 55 144 377 987 2584 6765 17711
A005563 \(\sum_{k=0}^{2} T_{2, k}\ n^k\) ➤ PolyRow2 ➤ -1 0 3 8 15 24 35 48 63 80 99 120 143
---------- \(\sum_{k=0}^{2} T_{2, n-k}\ n^k\) ➤ RevPolyRow2 ➤ 1 0 -3 -8 -15 -24 -35 -48 -63 -80 -99
A005809 \(T_{2 n, n}\) ➤ CentralE ➤ 1 0 -3 0 15 0 -84 0 495 0 -3003 0 18564
A011655 \(\sum_{k=0}^{n} T_{n, k}\) ➤ TablSum ➤ 1 1 0 -1 -1 0 1 1 0 -1 -1 0 1 1 0 -1 -1
---------- \(\sum_{k=0}^{n} T_{n, k}\ (-1)^{k}\) ➤ AltSum ➤ 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1
---------- \(\sum_{k=0}^{n} T_{n, n-k}\ [2 | k]\) ➤ RevEvenSum ➤ 1 1 0 -1 -1 0 1 1 0 -1 -1 0 1 1 0 -1 -1
A025560 \(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 1 2 3 12 30 60 210 840 1260 2520
A045721 \(T_{2 n + 1, n}\) ➤ RevCentralO ➤ 1 0 -4 0 21 0 -120 0 715 0 -4368 0
A052173 \(T^{-1}_{n, n - k}\) ➤ Trevinv ➤ 1 1 0 1 0 1 1 0 2 0 1 0 3 0 2 1 0 4 0 5
A053121 \(T^{-1}_{n, k}\) ➤ Tinv ➤ 1 0 1 1 0 1 0 2 0 1 2 0 3 0 1 0 5 0 4 0
A056220 \(\sum_{k=0}^{3} T_{3, n-k}\ n^k\) ➤ RevPolyRow3 ➤ 1 -1 -7 -17 -31 -49 -71 -97 -127 -161
A073028 \(\text{max}_{k=0}^{n}\ | T_{n, k} |\) ➤ TablMax ➤ 1 1 1 2 3 4 6 10 15 21 35 56 84 126 210
A097690 \(\sum_{k=0}^{n} T_{n, k}\ n^k\) ➤ PolyDiag ➤ 1 1 3 21 209 2640 40391 726103 15003009
A099530 \(\sum_{k=0}^{n/2} T_{n - k, n-k}\) ➤ RevAntiDSum ➤ 1 1 1 1 0 -1 -2 -3 -3 -2 0 3 6 8 8 5 -1
A106853 \(\sum_{k=0}^{n} T_{n, k} \ 2^{n - k} \) ➤ PosHalf ➤ 1 1 -3 -7 5 33 13 -119 -171 305 989
---------- \(\sum_{k=0}^{n} T_{n, k} \ (-2)^{n - k} \) ➤ NegHalf ➤ 1 1 -3 -7 5 33 13 -119 -171 305 989
A112552 \(T_{n + 1, k + 1} \) ➤ Toff11 ➤ 1 0 1 -2 0 1 0 -3 0 1 3 0 -4 0 1 0 6 0
A112554 \(T^{-1}_{n + 1, k + 1}\) ➤ Tinv11 ➤ 1 0 1 2 0 1 0 3 0 1 5 0 4 0 1 0 9 0 5 0
A142150 \(T_{n + 1, 1}\) ➤ TablCol1 ➤ 1 0 -2 0 3 0 -4 0 5 0 -6 0 7 0 -8 0 9 0
A146078 \(\sum_{k=0}^{n} T_{n, n-k}\ 3^k\) ➤ RevPolyCol3 ➤ 1 1 -8 -17 55 208 -287 -2159 424 19855
A162515 \(T_{n, n - k}\) ➤ Trev ➤ 1 1 0 1 0 -1 1 0 -2 0 1 0 -3 0 1 1 0 -4
---------- \(T_{n, n-k}\ (-1)^{n-k}\) ➤ RevTalt ➤ 1 1 0 1 0 -1 1 0 -2 0 1 0 -3 0 1 1 0 -4
A165817 \(T_{2 n + 1, n}\) ➤ CentralO ➤ 0 -2 0 10 0 -56 0 330 0 -2002 0 12376 0
A168561 \(T_{n, k}\) ➤ Triangle ➤ 1 0 1 -1 0 1 0 -2 0 1 1 0 -3 0 1 0 3 0
---------- \(T_{n, k}\ (-1)^{k}\) ➤ Talt ➤ 1 0 -1 -1 0 1 0 2 0 -1 1 0 -3 0 1 0 -3
A180184 \(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 1 0 1 0 1 0 -1 1 0 -2 1 0 -3 0 1 0
A186731 \(\sum_{k=0}^{n} T_{n, k} \ k\) ➤ TransNat0 ➤ 0 1 2 1 -2 -4 -2 3 6 3 -4 -8 -4 5 10 5
A242135 \(\sum_{k=0}^{3} T_{3, k}\ n^k\) ➤ PolyRow3 ➤ 0 -1 4 21 56 115 204 329 496 711 980
A257000 \(\sum_{k=0}^{n} T_{n, k}\ [2 | k]\) ➤ EvenSum ➤ 1 0 0 0 -1 0 1 0 0 0 -1 0 1 0 0 0 -1 0
---------- \(\sum_{k=0}^{n} T_{n, k}\ (1 - [2 | k])\) ➤ OddSum ➤ 0 1 0 -1 0 0 0 1 0 -1 0 0 0 1 0 -1 0 0
A278415 \(\sum_{k=0}^{n} T_{n, k} \ \binom{n}{k} \) ➤ BinConv ➤ 1 1 0 -5 -16 -24 15 197 576 724 -1200
---------- \(\sum_{k=0}^{n} T_{n, k} \ (-1)^{n - k} \ \binom{n}{k} \) ➤ InvBinConv ➤ 1 1 0 -5 -16 -24 15 197 576 724 -1200
A294519 \(T_{n + 1, k + 1}\ (k + 1) \) ➤ Tder ➤ 1 0 2 -2 0 3 0 -6 0 4 3 0 -12 0 5 0 12