A344437 Regular triangle read by rows, T(n,k) is the number of derangements of [n] with exactly k right-to-left minima, for n >= 2 and 1 <= k <= n-1.
1, 1, 1, 3, 5, 1, 11, 21, 11, 1, 53, 113, 79, 19, 1, 309, 715, 589, 211, 29, 1, 2119, 5235, 4835, 2141, 461, 41, 1, 16687, 43507, 43831, 22357, 6175, 883, 55, 1, 148329, 404699, 437079, 247549, 80531, 15161, 1541, 71, 1, 1468457, 4165965, 4765971, 2931193, 1074701, 242617, 33067, 2509, 89, 1
Offset: 2
Examples
1;
1, 1;
3, 5, 1;
11, 21, 11, 1;
53, 113, 79, 19, 1;
309, 715, 589, 211, 29, 1;
2119, 5235, 4835, 2141, 461, 41, 1;
...
Links
- Alois P. Heinz, Rows n = 2..23, flattened
- Per Alexandersson and Frether Getachew, An involution on derangements, arXiv:2105.08455 [math.CO], 2021.
- Yanni Pei and Jiang Zeng, Counting signed derangements with right-to-left minima and excedances, arXiv:2206.11236 [math.CO], 2022.
Formula
Sum_{k=1..n-1} k * T(n,k) = A344455(n). - Alois P. Heinz, May 19 2021
Extensions
More terms (rows 9-11) from Alois P. Heinz, May 19 2021