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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)). 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 Cf. A003221, A145219, A145223. Sequence in context: A044478 A228319 A236474 * A234266 A234259 A135286 Adjacent sequences:  A145217 A145218 A145219 * A145221 A145222 A145223 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 June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)