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A129817
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Number of alternating fixed-point-free permutations on n letters.
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3
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0, 1, 1, 2, 6, 24, 102, 528, 2952, 19008, 131112, 1009728, 8271792, 74167488, 703077552, 7194754368, 77437418112, 890643066048, 10726837356672, 136988469649728
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| For n>0 a(2n-1)=A129815(2n-1); for n>1 a(2n)=A129815(2n)+ A129815(2n-2). - Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 29 2008
We conjecture that for n>=3, A000111(2n)/a(2n) < e < A000111(2n)/A129815(2n), so that A000111(2n)/a(2n) increases while A000111(2n)/A129815(2n) decreases (and both quotients tend to e) - Vladimir Shevelev (shevelev(AT)bgu.ac.il), Apr 29 2008
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 06 2009: (Start)
Alternating permutations are called also down-up permutations.
a(n) is also the number of alternating permutations of {1,2,...n} having exactly 1 fixed point (see the Richard Stanley reference). Example: a(4)=2 because we gave 4132 and 3241.
(End)
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LINKS
| R. P. Stanley, Alternating permutations and symmetric functions
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EXAMPLE
| Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 06 2009: (Start)
a(4)=2 because we have 3142 and 2143.
(End)
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CROSSREFS
| Cf. A000111, A000166, A007779.
Sequence in context: A094012 A141253 A078486 * A128652 A152316 A177520
Adjacent sequences: A129814 A129815 A129816 * A129818 A129819 A129820
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KEYWORD
| more,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), May 20 2007
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