This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A121703 #13 Jul 07 2024 13:49:51
%S A121703 1,2,4,8,20,48,132,344,996,2720,8132,22888,69940,201040,624132,
%T A121703 1822136,5725124,16915008,53648772,160012232,511360340,1536928624,
%U A121703 4942300804,14949122328,48322714020,146946942688,477105960772,1457491035944,4750171491956,14568377075344
%N A121703 Number of alternating separable permutations.
%C A121703 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 A121703 Robert Brignall, Sophie Huczynska, and Vincent Vatter, <a href="https://arxiv.org/abs/math/0608391">Simple permutations and algebraic generating functions</a>, arXiv:math/0608391 [math.CO], 2006.
%F A121703 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 A121703 a(4)=8 because of the 10 alternating permutations of length 4, 2413 and 3142 are not separable.
%t A121703 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 *)
%Y A121703 Cf. A121704.
%K A121703 nonn
%O A121703 1,2
%A A121703 _Vincent Vatter_, Aug 16 2006
%E A121703 a(13) and beyond corrected by _Vaclav Kotesovec_, Jul 07 2024