

A129817


Number of alternating fixedpointfree permutations on n letters.


3



1, 0, 1, 1, 2, 6, 24, 102, 528, 2952, 19008, 131112, 1009728, 8271792, 74167488, 703077552, 7194754368, 77437418112, 890643066048, 10726837356672, 136988469649728, 1825110309733632
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OFFSET

0,5


COMMENTS

For n > 0, a(2n1) = A129815(2n1); for n > 1, a(2n) = A129815(2n) + A129815(2n2).  Vladimir Shevelev, 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, Apr 29 2008
From Emeric Deutsch, Aug 06 2009: (Start)
Alternating permutations are also called downup 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)


LINKS

Table of n, a(n) for n=0..21.
R. P. Stanley, Alternating permutations and symmetric functions, arXiv:math/0603520 [math.CO], 2006.


FORMULA

a(n) = A162979(n,0).  Alois P. Heinz, Nov 24 2017


EXAMPLE

a(4)=2 because we have 3142 and 2143.  Emeric Deutsch, Aug 06 2009


CROSSREFS

Cf. A000111, A000166, A007779.
Column k=0 of A162979.
Sequence in context: A094012 A141253 A078486 * A230797 A128652 A152316
Adjacent sequences: A129814 A129815 A129816 * A129818 A129819 A129820


KEYWORD

more,nonn


AUTHOR

Vladeta Jovovic, May 20 2007


EXTENSIONS

a(21) from Alois P. Heinz, Nov 06 2015
a(0)=1 prepended by Alois P. Heinz, Nov 24 2017


STATUS

approved



