A377660 Triangle read by rows: T(n, k) = (n - k)!*(n + k)!/n!.

1, 1, 2, 2, 3, 12, 6, 8, 20, 120, 24, 30, 60, 210, 1680, 120, 144, 252, 672, 3024, 30240, 720, 840, 1344, 3024, 10080, 55440, 665280, 5040, 5760, 8640, 17280, 47520, 190080, 1235520, 17297280, 40320, 45360, 64800, 118800, 285120, 926640, 4324320, 32432400, 518918400

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

Triangle starts:
  [0]   1;
  [1]   1,   2;
  [2]   2,   3,   12;
  [3]   6,   8,   20,  120;
  [4]  24,  30,   60,  210,  1680;
  [5] 120, 144,  252,  672,  3024, 30240;
  [6] 720, 840, 1344, 3024, 10080, 55440, 665280;

Maple

T := (n, k) -> (n-k)!*(n+k)!/n!: seq(seq(T(n, k), k= 0..n), n = 0..8);

Mathematica

Table[(n-k)! (n+k)!/n!, {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Feb 17 2025 *)

Crossrefs

Cf. A000142, A001813.

Sequence in context: A134243 A182779 A199673 * A375218 A335942 A240133

Adjacent sequences: A377657 A377658 A377659 * A377661 A377662 A377663

Keyword

nonn,tabl

Author

Peter Luschny, Dec 08 2024

Status

approved