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Search: id:A003221
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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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+0
7
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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; listen)
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OFFSET
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0,4
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REFERENCES
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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]
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
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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
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a(n)=(A000166(n)-(-1)^n*(n-1))/2.
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CROSSREFS
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Cf. A000166.
Sequence in context: A009231 A012304 A047157 this_sequence A013312 A013318 A048674
Adjacent sequences: A003218 A003219 A003220 this_sequence A003222 A003223 A003224
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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