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

2,4

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

Example

     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;
  ...

Crossrefs

Row sums give A000166.

Cf. A000255 (column 1), A028387, A132393, A344455.

Sequence in context: A259182 A138259 A077021 * A143250 A221494 A174883

Adjacent sequences: A344434 A344435 A344436 * A344438 A344439 A344440

Keyword

nonn,tabl

Author

Michel Marcus, May 19 2021

Extensions

More terms (rows 9-11) from Alois P. Heinz, May 19 2021

Status

approved