A344437 - OEIS

%I #22 Jun 23 2022 07:05:09

%S 1,1,1,3,5,1,11,21,11,1,53,113,79,19,1,309,715,589,211,29,1,2119,5235,

%T 4835,2141,461,41,1,16687,43507,43831,22357,6175,883,55,1,148329,

%U 404699,437079,247549,80531,15161,1541,71,1,1468457,4165965,4765971,2931193,1074701,242617,33067,2509,89,1

%N 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.

%H Alois P. Heinz, <a href="/A344437/b344437.txt">Rows n = 2..23, flattened</a>

%H Per Alexandersson and Frether Getachew, <a href="https://arxiv.org/abs/2105.08455">An involution on derangements</a>, arXiv:2105.08455 [math.CO], 2021.

%H Yanni Pei and Jiang Zeng, <a href="https://arxiv.org/abs/2206.11236">Counting signed derangements with right-to-left minima and excedances</a>, arXiv:2206.11236 [math.CO], 2022.

%F Sum_{k=1..n-1} k * T(n,k) = A344455(n). - _Alois P. Heinz_, May 19 2021

%e      1;

%e      1,    1;

%e      3,    5,    1;

%e     11,   21,   11,    1;

%e     53,  113,   79,   19,   1;

%e    309,  715,  589,  211,  29,  1;

%e   2119, 5235, 4835, 2141, 461, 41, 1;

%e   ...

%Y Row sums give A000166.

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

%K nonn,tabl

%O 2,4

%A _Michel Marcus_, May 19 2021

%E More terms (rows 9-11) from _Alois P. Heinz_, May 19 2021