A364817 Triangle read by rows: T(n,k) = number of permutations p of [n] such that max(|p(p(i)) - i|)=k (n>=1, 0<=k<=n-1).

1, 2, 0, 4, 0, 2, 10, 2, 6, 6, 26, 6, 22, 36, 30, 76, 24, 92, 144, 216, 168, 232, 80, 334, 640, 1150, 1524, 1080, 764, 312, 1328, 2984, 5516, 9712, 11784, 7920, 2620, 1152, 5234, 13296, 27668, 55750, 90240, 101400, 65520, 9496, 4616, 21780, 62124, 144564, 306272, 601756, 909312, 964080, 604800

Offset: 1

Author

Seiichi Manyama, Oct 21 2023

Keywords

• nonn
• tabl

Examples

			Triangle starts:
     1;
     2,    0;
     4,    0,    2;
    10,    2,    6,     6;
    26,    6,   22,    36,    30;
    76,   24,   92,   144,   216,   168;
   232,   80,  334,   640,  1150,  1524,  1080;
   764,  312, 1328,  2984,  5516,  9712, 11784,   7920;
  2620, 1152, 5234, 13296, 27668, 55750, 90240, 101400, 65520;
		

Crossrefs

Columns k=0..1 give: A000085, A364819.

Row sums give A000142.

Cf. A130152, A175925.

Formula

T(n,n-1) = (2*n-5)*(n-2)! for n>3.