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

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