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A145225 T(n,k) is the number of odd permutations (of an n-set) with exactly k fixed points. 0
0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 6, 0, 6, 0, 0, 20, 30, 0, 10, 0, 0, 135, 120, 90, 0, 15, 0, 0, 924, 945, 420, 210, 0, 21, 0, 0, 7420, 7392, 3780, 1120, 420, 0, 28, 0, 0, 66744, 66780, 33264, 11340, 2520, 756, 0, 36, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

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)*A145221(n-k)

E.g.f.: (x^(k+2)*exp(-x))/(2*(k!)*(1-x)).

EXAMPLE

Triangle starts:

0;

0, 0;

1, 0, 0;

0, 3, 0, 0;

6, 0, 6, 0, 0;

20, 30, 0, 10, 0;

...

CROSSREFS

Row sum is A001710 for n > 1, sum of Row1=sum of Row2 = 0.

T(n, 0) is A145221, T(n, 1) is A145222, T(n, 2) is A145223.

Sequence in context: A062688 A067181 A321429 * A061480 A220692 A048962

Adjacent sequences:  A145222 A145223 A145224 * A145226 A145227 A145228

KEYWORD

nonn,tabl

AUTHOR

Abdullahi Umar, Oct 10 2008

STATUS

approved

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Last modified June 26 04:02 EDT 2019. Contains 324368 sequences. (Running on oeis4.)