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A003221
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Number of even permutations of length n with no fixed points.
(Formerly M0922)
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6
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1, 0, 0, 2, 3, 24, 130, 930, 7413, 66752, 667476, 7342290, 88107415, 1145396472, 16035550518, 240533257874, 3848532125865, 65425046139840, 1177650830516968, 22375365779822562, 447507315596451051, 9397653627525472280, 206748379805560389930
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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. [From A. Umar (aumarh(AT)squ.edu.om), Oct 09 2008]
G. Gordon and E. McMahon, Moving faces to other places: facet derangements, Amer. Math. Monthly, 117 (2010), 865-88.
Problem E2354, Amer. Math. Monthly, 79 (1972), 394.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| Contribution from A. Umar (aumarh(AT)squ.edu.om), Oct 09 2008: (Start)
a(n)=(n!/2)sum(i=0,n-2,((-1)^i)/i!)+((-1)^(n-1))(n-1),(n>1),a(0)=1, a(1)=0;
a(n)=(n-1)(a(n-1)+a(n-2)))+((-1)^(n-1))(n-1), a(0)=1, a(1)=0;
a(n)=na(n-1)+((-1)^(n-1))(n-2)(n+1)/2, a(0)=1.
Egf. (1-x^2/2)e^(-x)/(1-x). (End)
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MAPLE
| a(n)=(A000166(n)-(-1)^n*(n-1))/2.
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MATHEMATICA
| a[n_] := (Round[n!/E] - (-1)^n*(n - 1))/2; a[0] = 1; Table[a[n], {n, 0, 22}] (* From Jean-François Alcover, Dec 13 2011, after Simon Plouffe *)
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CROSSREFS
| Cf. A000166, A000387.
Sequence in context: A009231 A012304 A047157 * A013312 A013318 A193338
Adjacent sequences: A003218 A003219 A003220 * A003222 A003223 A003224
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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