A145224 Triangle read by rows: T(n,k) is the number of even permutations (of an n-set) with exactly k fixed points.

1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 3, 8, 0, 0, 1, 24, 15, 20, 0, 0, 1, 130, 144, 45, 40, 0, 0, 1, 930, 910, 504, 105, 70, 0, 0, 1, 7413, 7440, 3640, 1344, 210, 112, 0, 0, 1, 66752, 66717, 33480, 10920, 3024, 378, 168, 0, 0, 1

Offset: 0

Author

Abdullahi Umar, Oct 09 2008

Keywords

• nonn
• tabl

Examples

			Triangle starts:
   1;
   0,  1;
   0,  0,  1;
   2,  0,  0, 1;
   3,  8,  0, 0, 1;
  24, 15, 20, 0, 0, 1;
  ...
		

Links

• Bashir Ali and A. Umar, Some combinatorial properties of the alternating group, Southeast Asian Bulletin Math. 32 (2008), 823-830.

Crossrefs

Row sums give A001710.

Columns k=0..2 are A003221, A145219, A145220.

Cf. A008290, A055137.

Formula

T(n,k) = C(n,k)*A003221(n-k).

E.g.f.: (x^k(1-x^2/2) e^(-x))/k!(1-x).

T(n,k) + A145225(n,k) = A008290(n,k). - R. J. Mathar, Jul 06 2023

T(n,k) = (A008290(n,k) + A055137(n,k))/2. - Julian Hatfield Iacoponi, Aug 08 2024