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%I #11 Aug 24 2023 11:54:10
%S 0,0,1,2,6,22,102,506,2952,18502,131112,991226,8271792,73176262,
%T 703077552,7121578106,77437418112,883521487942,10726837356672,
%U 136104948161786,1825110309733632
%N Number of reverse alternating fixed-point-free permutations on n letters.
%C From _Emeric Deutsch_, Aug 06 2009: (Start)
%C Reverse alternating permutations are called also up-down permutations.
%C 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.
%C (End)
%H R. P. Stanley, <a href="https://arxiv.org/abs/math/0603520">Alternating permutations and symmetric functions</a>, arXiv:math/0603520 [math.CO], 2006.
%F a(2n-1) = A129817(2n-1). [_Emeric Deutsch_, Aug 06 2009]
%e a(4)=2 because we have 3412 and 2413. [_Emeric Deutsch_, Aug 06 2009]
%Y Cf. A000111, A000166, A007779, A129817.
%K more,nonn
%O 1,4
%A _Vladeta Jovovic_, May 20 2007
%E a(21) from _Alois P. Heinz_, Jun 11 2015
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