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A145222 a(n) is the number of odd permutations (of an n-set) with exactly 1 fixed point. 3
0, 0, 3, 0, 30, 120, 945, 7392, 66780, 667440, 7342335, 88107360, 1145396538, 16035550440, 240533257965, 3848532125760, 65425046139960, 1177650830516832, 22375365779822715, 447507315596450880, 9397653627525472470, 206748379805560389720, 4755212735527888968873 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..23.

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

FORMULA

a(n) = n*A145221(n-1), (n > 0).

E.g.f.: ((x^3)*exp(-x))/(2*(1-x)).

EXAMPLE

a(3) = 3 because there are exactly 3 odd permutations (of a 3-set) having 1 fixed point, namely: (12), (13), (23).

PROG

(PARI) x = 'x + O('x^30); Vec(serlaplace(((x^3)*exp(-x))/(2*(1-x)))) \\ Michel Marcus, Apr 04 2016

CROSSREFS

Cf. A000387 (odd permutations with no fixed points), A145219 (even permutations with exactly 1 fixed point), A145223 (odd permutations with exactly 2 fixed points).

Sequence in context: A215586 A215680 A007415 * A058833 A266168 A276913

Adjacent sequences:  A145219 A145220 A145221 * A145223 A145224 A145225

KEYWORD

nonn

AUTHOR

Abdullahi Umar, Oct 09 2008

EXTENSIONS

More terms from Alois P. Heinz, Apr 04 2016

STATUS

approved

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Last modified October 23 08:57 EDT 2019. Contains 328345 sequences. (Running on oeis4.)