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A145223
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a(n) is the number of odd permutations (of an n-set) with exactly 2 fixed points.
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3
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0, 0, 6, 0, 90, 420, 3780, 33264, 333900, 3670920, 44054010, 572697840, 8017775766, 120266628300, 1924266063720, 32712523068960, 588825415259640, 11187682889909904, 223753657798227150, 4698826813762734240, 103374189902780197170, 2377606367763944481780
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OFFSET
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2,3
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LINKS
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FORMULA
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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
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EXAMPLE
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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).
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MAPLE
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egf:= x^4 * exp(-x)/(4*(1-x));
a:= n-> n! * coeff(series(egf, x, n+1), x, n):
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PROG
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(PARI) x = 'x + O('x^30); Vec(serlaplace(((x^4)*exp(-x))/(4*(1-x)))) \\ Michel Marcus, Apr 04 2016
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CROSSREFS
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Cf. A000387 (odd permutations with no fixed points), A145222 (odd permutations with exactly 1 fixed point, A145220 (even permutations with exactly 2 fixed points).
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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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