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%I #5 Mar 31 2012 20:08:09
%S 1,2,4,8,20,48,132,344,996,2720,8132,22888,69941,201029,624077,
%T 1821359,5722885,16919312,53779406,159276786
%N Number of alternating separable permutations.
%C The separable permutations are those avoiding 2413 and 3142 and are counted by the large Schroeder numbers (A006318). The alternating permutations are counted by the Euler numbers (A000111).
%H R. Brignall, S. Huczynska and V. Vatter, <a href="http://arXiv.org/abs/math.CO/0608391">Simple permutations and algebraic generating functions</a>, arXiv:math.CO/0608391.
%F G.f. satisfies f^3-(2x^2-5x+4)f^2-(4x^3+x^2-8x)f-(2x^4+5x^3+4x^2)=0.
%e a(4)=8 because of the 10 alternating permutations of length 4, 2413 and 3142 are not separable.
%Y Cf. A121704.
%K nonn
%O 1,2
%A _Vincent Vatter_, Aug 16 2006
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