Partition
A072233 \(\bbox[yellow, 5px]{\color{DarkGreen} T_{n, k} \ = \ T_{n - 1, k - 1} + T_{n - k, k} } \)
\(T^{-1}_{n, k}\) ➤ Tinv ➤ 1 0 1 0 -1 1 0 0 -1 1 0 1 -1 -1 1 0 0 1
\(T_{n, n - k}\) ➤ Trev ➤ 1 1 0 1 1 0 1 1 1 0 1 1 2 1 0 1 1 2 2 1
\(T^{-1}_{n + 1, n - k + 1}\) ➤ Trevinv11 ➤ 1 1 -1 1 -1 0 1 -1 -1 1 1 -1 -1 1 0 1
\((T_{n + 1, n - k + 1})^{-1}\) ➤ Tinvrev11 ➤ 1 -1 1 0 -1 1 0 1 -2 1 0 -1 2 -2 1 0 1
\(T_{n - k, k} \ \ (k \le n/2)\) ➤ Tantidiag ➤ 1 0 0 1 0 1 0 1 1 0 1 1 0 1 2 1 0 1 2 1
\(\sum_{j=0}^{k} T_{n, j}\) ➤ Tacc ➤ 1 0 1 0 1 2 0 1 2 3 0 1 3 4 5 0 1 3 5 6
\(\text{lcm}_{k=0}^{n}\ | T_{n, k} |\ \ (T_{n,k}>1)\) ➤ TablLcm ➤ 1 1 1 1 2 2 6 12 60 420 2520 2310 60060
\(\sum_{k=0}^{n} T_{n, k} \ (-1)^{n - k} \ \binom{n}{k} \) ➤ InvBinConv ➤ 1 1 -1 1 5 1 4 15 55 139 152 397 1429
\(T_{n + 1, n-k} \) ➤ RevToff11 ➤ 0 1 0 1 1 0 1 2 1 0 1 2 2 1 0 1 2 3 3 1
\(T_{n + 1, n-k} \) ➤ RevTrev11 ➤ 0 0 1 0 1 1 0 1 2 1 0 1 2 2 1 0 1 3 3 2
\(T_{n - k, n - 2k} \ \ (k \le n/2)\) ➤ RevTantidiag ➤ 1 1 1 0 1 1 1 1 0 1 1 1 1 1 2 0 1 1 2 1
\(\sum_{j=0}^{n-k} T_{n, n-j}\) ➤ RevTacc ➤ 1 1 1 1 2 2 1 2 3 3 1 2 4 5 5 1 2 4 6 7
\(T_{n, n-k}\ (-1)^{n-k}\) ➤ RevTalt ➤ 1 1 0 1 -1 0 1 -1 1 0 1 -1 2 -1 0 1 -1
\(T_{n + 1, n-k}\ (n-k + 1) \) ➤ RevTder ➤ 0 1 0 1 2 0 1 4 3 0 1 4 6 4 0 1 4 9 12
\(\sum_{k=0}^{n} T_{n, n-k}\ k^{2}\) ➤ RevTransSqrs ➤ 0 0 1 5 18 43 109 211 434 778 1408 2335