A145224 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,7

LINKS

Table of n, a(n) for n=0..54.

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

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

EXAMPLE