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).

Table of n, a(n) for n=1..20.

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: A338197 A056952 A225585 * A301467 A275070 A115219

Adjacent sequences: A121700 A121701 A121702 * A121704 A121705 A121706

nonn

Vincent Vatter, Aug 16 2006

approved