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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.

%I A344437 #22 Jun 23 2022 07:05:09
%S A344437 1,1,1,3,5,1,11,21,11,1,53,113,79,19,1,309,715,589,211,29,1,2119,5235,
%T A344437 4835,2141,461,41,1,16687,43507,43831,22357,6175,883,55,1,148329,
%U A344437 404699,437079,247549,80531,15161,1541,71,1,1468457,4165965,4765971,2931193,1074701,242617,33067,2509,89,1
%N 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.
%H A344437 Alois P. Heinz, <a href="/A344437/b344437.txt">Rows n = 2..23, flattened</a>
%H A344437 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 A344437 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 A344437 Sum_{k=1..n-1} k * T(n,k) = A344455(n). - _Alois P. Heinz_, May 19 2021
%e A344437      1;
%e A344437      1,    1;
%e A344437      3,    5,    1;
%e A344437     11,   21,   11,    1;
%e A344437     53,  113,   79,   19,   1;
%e A344437    309,  715,  589,  211,  29,  1;
%e A344437   2119, 5235, 4835, 2141, 461, 41, 1;
%e A344437   ...
%Y A344437 Row sums give A000166.
%Y A344437 Cf. A000255 (column 1), A028387, A132393, A344455.
%K A344437 nonn,tabl
%O A344437 2,4
%A A344437 _Michel Marcus_, May 19 2021
%E A344437 More terms (rows 9-11) from _Alois P. Heinz_, May 19 2021