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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) = A145225(n,2) = (n*(n-1)/2) * A000387(n-2), (n > 1). E.g.f.: x^4*exp(-x)/(4*(1-x)). D-finite with recurrence +(-n+6)*a(n) +(n-2)*(n-7)*a(n-1) +(n-2)*(n-3)*a(n-2)=0. - R. J. Mathar, Jul 06 2023 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: A057399 A245086 A365909 * A365979 A219948 A072129 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 August 13 14:39 EDT 2024. Contains 375142 sequences. (Running on oeis4.)