1,2
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).
R. Brignall, S. Huczynska and V. Vatter, Simple permutations and algebraic generating functions, arXiv:math.CO/0608391.
G.f. satisfies f^3-(2x^2-5x+4)f^2-(4x^3+x^2-8x)f-(2x^4+5x^3+4x^2)=0.
a(4)=8 because of the 10 alternating permutations of length 4, 2413 and 3142 are not separable.
Cf. A121704.
Sequence in context: A051389 A078006 A056952 * A115219 A078160 A089976
Adjacent sequences: A121700 A121701 A121702 * A121704 A121705 A121706
nonn
Vince Vatter (vince(AT)mcs.st-and.ac.uk), Aug 16 2006
