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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Problem E2354, Amer. Math. Monthly, 79 (1972), 394.
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]
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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.
Adjacent sequences: A003218 A003219 A003220 this_sequence A003222 A003223 A003224
Sequence in context: A009231 A012304 A047157 this_sequence A013312 A013318 A048674
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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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