A129815 Number of reverse alternating fixed-point-free permutations on n letters.

0, 0, 1, 2, 6, 22, 102, 506, 2952, 18502, 131112, 991226, 8271792, 73176262, 703077552, 7121578106, 77437418112, 883521487942, 10726837356672, 136104948161786, 1825110309733632

Offset

1,4

Comments

From Emeric Deutsch, Aug 06 2009: (Start)

Reverse alternating permutations are called also up-down permutations.

a(n) is also the number of reverse alternating permutations having exactly 1 fixed point (see the Stanley reference). Example: a(4)=2 because we have 1423 and 2314.

(End)

Links

Table of n, a(n) for n=1..21.

R. P. Stanley, Alternating permutations and symmetric functions, arXiv:math/0603520 [math.CO], 2006.

Formula

a(2n-1) = A129817(2n-1). [Emeric Deutsch, Aug 06 2009]

Example

a(4)=2 because we have 3412 and 2413. [Emeric Deutsch, Aug 06 2009]

Crossrefs

Cf. A000111, A000166, A007779, A129817.

Sequence in context: A002772 A000140 A079263 * A345194 A251181 A309579

Adjacent sequences: A129812 A129813 A129814 * A129816 A129817 A129818

Keyword

more,nonn

Author

Vladeta Jovovic, May 20 2007

Extensions

a(21) from Alois P. Heinz, Jun 11 2015

Status

approved