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A145220 a(n) is the number of even permutations (of an n-set) with exactly 2 fixed points. 3
1, 0, 0, 20, 45, 504, 3640, 33480, 333585, 3671360, 44053416, 572698620, 8017774765, 120266629560, 1924266062160, 32712523070864, 588825415257345, 11187682889912640, 223753657798223920, 4698826813762738020, 103374189902780192781, 2377606367763944486840 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,4
LINKS
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)*A003221(n-2), (n > 1).
E.g.f.: (x^2*(1-x^2/2) * exp(-x))/(2*(1-x)).
D-finite with recurrence -(n-5)*(n-2)^2*a(n) +n*(n-3)*(n^2-7*n+8)*a(n-1) +n*(n-4)*(n-1)^2*a(n-2)=0. - R. J. Mathar, Jul 06 2023
EXAMPLE
a(5) = 20 because there are exactly 20 even permutations (of a 5-set) having 2 fixed points, namely: (123), (132), (124), (142), (125), (152), (134), (143), (135), (153), (145), (154), (234), (243), (235), (253), (245), (254), (345), (354).
PROG
(PARI) x = 'x + O('x^30); Vec(serlaplace((x^2*(1-x^2/2) * exp(-x))/(2*(1-x)))) \\ Michel Marcus, Apr 04 2016
CROSSREFS
Sequence in context: A044478 A228319 A236474 * A234266 A234259 A135286
KEYWORD
nonn
AUTHOR
Abdullahi Umar, Oct 09 2008
EXTENSIONS
More terms from Alois P. Heinz, Nov 19 2013
STATUS
approved

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)