A143216 Triangle read by rows: T(n,k) = n!*k!, 0 <= k <= n.

1, 1, 1, 2, 2, 4, 6, 6, 12, 36, 24, 24, 48, 144, 576, 120, 120, 240, 720, 2880, 14400, 720, 720, 1440, 4320, 17280, 86400, 518400, 5040, 5040, 10080, 30240, 120960, 604800, 3628800, 25401600, 40320, 40320, 80640, 241920, 967680, 4838400, 29030400, 203212800, 1625702400

Offset: 0

Author

Gary W. Adamson, Jul 30 2008

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle =
    1;
    1,   1;
    2,   2,    4;
    6,   6,   12,   36;
   24,  24,   48,  144,   576;
  120, 120,  240,  720,  2880, 14400;
  720, 720, 1440, 4320, 17280, 86400, 518400;
  ...
T(6,3) = 4320 = 6!*3! = 720*6.
		

Links

• Stefano Spezia, First 101 rows of the triangle, flattened

Crossrefs

Cf. A000142, A098361 (as an array), A143217 (row sums).

Programs

Magma

F:=Factorial; [F(n)*F(k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 12 2022

Mathematica

Table[n!k!,{n,0,8},{k,0,n}] (* Stefano Spezia, Jul 09 2020 *)

SageMath

f=factorial; flatten([[f(n)*f(k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 12 2022

Formula

T(n,k) = n!*k!, 0 <= k <= n.

E.g.f.: 1/((1 - x)*(1 - y)). - Stefano Spezia, Jul 09 2020