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A145220
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a(n) is the number of even permutations (of an n-set) with exactly 2 fixed points.
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3
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1, 0, 0, 20, 45, 504, 3640, 33480, 333585, 3671360, 44053416, 572698620, 8017774765, 120266629560, 1924266062160, 32712523070864, 588825415257345, 11187682889912640, 223753657798223920, 4698826813762738020, 103374189902780192781, 2377606367763944486840
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OFFSET
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2,4
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LINKS
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FORMULA
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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
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EXAMPLE
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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).
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PROG
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(PARI) x = 'x + O('x^30); Vec(serlaplace((x^2*(1-x^2/2) * exp(-x))/(2*(1-x)))) \\ Michel Marcus, Apr 04 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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