OFFSET
1,2
COMMENTS
LINKS
Robert Brignall, Sophie Huczynska, and Vincent Vatter, Simple permutations and algebraic generating functions, arXiv:math/0608391 [math.CO], 2006.
FORMULA
G.f. satisfies f^3-(2x^2-5x+4)f^2-(4x^3+x^2-8x)f-(2x^4+5x^3+4x^2)=0.
EXAMPLE
a(4)=8 because of the 10 alternating permutations of length 4, 2413 and 3142 are not separable.
MATHEMATICA
nmax = 40; aa = ConstantArray[0, nmax]; aa[[1]] = 1; aa[[2]] = 2; Do[f = Sum[aa[[k]]*x^k, {k, 1, j - 1}] + koef*x^j; sol = Solve[SeriesCoefficient[f^3 - (2*x^2 - 5*x + 4)*f^2 - (4*x^3 + x^2 - 8*x)*f - (2*x^4 + 5*x^3 + 4*x^2), {x, 0, j + 2}] == 0, koef][[1]]; aa[[j]] = koef /. sol[[1]], {j, 3, nmax}]; aa (* Vaclav Kotesovec, Jul 07 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vincent Vatter, Aug 16 2006
EXTENSIONS
a(13) and beyond corrected by Vaclav Kotesovec, Jul 07 2024
STATUS
approved