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

0,4

Links

Stefano Spezia, First 101 rows of the triangle, flattened

Formula

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A355649 A102425 A162608 * A086536 A053045 A152424

Adjacent sequences: A143213 A143214 A143215 * A143217 A143218 A143219

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 30 2008

Status

approved