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A145223 a(n) is the number of odd permutations (of an n-set) with exactly 2 fixed points. 3
0, 0, 6, 0, 90, 420, 3780, 33264, 333900, 3670920, 44054010, 572697840, 8017775766, 120266628300, 1924266063720, 32712523068960, 588825415259640, 11187682889909904, 223753657798227150, 4698826813762734240, 103374189902780197170, 2377606367763944481780 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..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*(n-1)/2) * A145221(n-2), (n > 1).

E.g.f.: ((x^4)*exp(-x))/(4*(1-x)).

EXAMPLE

a(4) = 6 because there are exactly 6 odd permutations (of a 4-set) having 2 fixed points, namely: (12), (13), (14), (23), (24), (34).

MAPLE

egf:= x^4 * exp(-x)/(4*(1-x));

a:= n-> n! * coeff(series(egf, x, n+1), x, n):

seq(a(n), n=2..30);  # Alois P. Heinz, Feb 01 2011

PROG

(PARI) x = 'x + O('x^30); Vec(serlaplace(((x^4)*exp(-x))/(4*(1-x)))) \\ Michel Marcus, Apr 04 2016

CROSSREFS

Cf. A000387 (odd permutations with no fixed points), A145222 (odd permutations with exactly 1 fixed point, A145220 (even permutations with exactly 2 fixed points).

Sequence in context: A156488 A057399 A245086 * A219948 A072129 A085511

Adjacent sequences:  A145220 A145221 A145222 * A145224 A145225 A145226

KEYWORD

nonn

AUTHOR

Abdullahi Umar, Oct 09 2008

EXTENSIONS

More terms from Alois P. Heinz, Feb 01 2011

STATUS

approved

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Last modified May 25 11:17 EDT 2019. Contains 323539 sequences. (Running on oeis4.)