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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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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REFERENCES
| Ali, Bashir and Umar, A., "Some combinatorial properties of the alternating group". Southeast Asian Bulletin Math. 32 (2008), 823-830.
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FORMULA
| a(n) = (n*(n-1)/2) * A145221(n-2), (n > 1).
E.g.f.: ((x^4)*exp(-x))/(4*(1-x)).
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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).
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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..25);
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CROSSREFS
| Cf. A145221.
Sequence in context: A199044 A156488 A057399 * A072129 A085511 A187525
Adjacent sequences: A145220 A145221 A145222 * A145224 A145225 A145226
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KEYWORD
| nonn
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AUTHOR
| A. Umar (aumarh(AT)squ.edu.om), Oct 09 2008
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EXTENSIONS
| More terms and Maple program from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Feb 01 2011
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