A371767 Triangle read by rows: T(n, k) = (k! * n!)/(n - k)!.

1, 1, 1, 1, 2, 4, 1, 3, 12, 36, 1, 4, 24, 144, 576, 1, 5, 40, 360, 2880, 14400, 1, 6, 60, 720, 8640, 86400, 518400, 1, 7, 84, 1260, 20160, 302400, 3628800, 25401600, 1, 8, 112, 2016, 40320, 806400, 14515200, 203212800, 1625702400

Offset: 0

Author

Peter Luschny, Apr 14 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
  [0] 1;
  [1] 1, 1;
  [2] 1, 2,  4;
  [3] 1, 3, 12,   36;
  [4] 1, 4, 24,  144,   576;
  [5] 1, 5, 40,  360,  2880,  14400;
  [6] 1, 6, 60,  720,  8640,  86400,  518400;
  [7] 1, 7, 84, 1260, 20160, 302400, 3628800, 25401600;
		

Crossrefs

Cf. A000142, A001044 (main diagonal), A010790 (subdiagonal), A046662 (row sums), A089041 (alternating row sums), A010050 (central terms).

Programs

Maple

T := (n, k) -> (k! * n!)/(n - k)!:
for n from 0 to 6 do seq(T(n, k), k = 0..n) od;