Moebius
A363914 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ M^{-1}(n, k); M(n, k) = [k \le n \ \& \ k | n] } \)
\(T^{-1}_{n, n - k}\) ➤ Trevinv ➤ 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 0 0 0 -1 -1 1 0 1
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 0 -1 0 0 -1 -1 0 0 0 -1 -1 0 0 -1
\(\sum_{k=0}^{n} T_{n, k} \ \binom{n}{k} \) ➤ BinConv ➤ 1 1 -1 -2 -5 -4 -28 -6 -69 -83 -286 -10
\(\sum_{k=0}^{n} T_{n, k} \ (-1)^{n - k} \ \binom{n}{k} \) ➤ InvBinConv ➤ 1 1 3 -2 -5 -4 0 -6 -69 -83 198 -10
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 -1 0 0 0
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 0 0 -1 0 -1 0 0 0 -1 0 0 -1 0 0 0 0 1
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0
\(T_{n, n-k}\ (-1)^{n-k}\) ➤ RevTalt ➤ 1 1 0 1 1 0 1 0 -1 0 1 0 -1 0 0 1 0 0 0
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 -1 0 0 -2 0 0 -2 0 0 0 0 0 -4 0 0 0
\(\sum_{k=0}^{n/2} T_{n - k, n-k}\) ➤ RevAntiDSum ➤ 1 1 1 0 1 0 0 1 1 -1 0 2 0 0 1 -1 1 1
\(\sum_{k=0}^{n} T_{n, n-k}\ (-2)^{n - k} \) ➤ RevNegHalf ➤ 1 -2 6 -6 12 -30 66 -126 240 -504 1050
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 0 -1 -4 -4 -16 0 -36 -16 -36 -8 -100
\(\sum_{k=0}^{n} T_{n, n-k}\ 3^k\) ➤ RevPolyCol3 ➤ 1 1 -2 -8 -8 -80 136 -728 -80 -728
\(\sum_{k=0}^{n} T_{n, n-k}\ n^k\) ➤ RevPolyDiag ➤ 1 1 -1 -8 -15 -624 6265 -117648 -4095