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 A165521 #14 Sep 08 2022 08:45:47
%S A165521 1,1,2,6,21,73,243,785,2504,7968,25389,81033,258873,827263,2643616,
%T A165521 8447300,26990489,86236655,275531223,880341121,2812760102,8987010878,
%U A165521 28714292671,91744697633,293132350135,936583428475,2992465580300
%N A165521 The number of 4321-avoiding separable permutations of length n.
%H A165521 G. C. Greubel, <a href="/A165521/b165521.txt">Table of n, a(n) for n = 0..1000</a>
%H A165521 D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 [math.CO] (2017), Table 2 No 102.
%H A165521 V. Vatter, <a href="https://doi.org/10.1016/j.jsc.2011.11.002">Finding regular insertion encodings for permutation classes</a>, Journal of Symbolic Computation, Volume 47, Issue 3, March 2012, Pages 259-265.
%H A165521 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,28,-23,12,-4,1).
%F A165521 G.f.: (1-x)^3*(1 -3*x +2*x^2 -x^3)/ (1 -7*x +19*x^2 -28*x^3 +23*x^4 -12*x^5 +4*x^6 -x^7).
%F A165521 The growth rate (limit of the n-th root of a(n)) is approximately 3.19508.
%e A165521 For n=6, there are 394 separable permutations; 243 of them avoid 4321.
%t A165521 CoefficientList[Series[(1 - x)^3*(1 -3*x +2*x^2 -x^3)/(1 -7*x +19*x^2 - 28*x^3 +23*x^4 -12*x^5 +4*x^6 -x^7), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 21 2018 *)
%o A165521 (PARI) x='x+O('x^50); Vec((1-x)^3*(1 -3*x +2*x^2 -x^3)/ (1 -7*x +19*x^2 -28*x^3 +23*x^4 -12*x^5 +4*x^6 -x^7)) \\ _G. C. Greubel_, Oct 21 2018
%o A165521 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)^3*(1 -3*x +2*x^2 -x^3)/ (1 -7*x +19*x^2 -28*x^3 +23*x^4 -12*x^5 +4*x^6 -x^7))); // _G. C. Greubel_, Oct 21 2018
%Y A165521 Cf. A034943, A165522, A165523.
%K A165521 nonn
%O A165521 0,3
%A A165521 _Vincent Vatter_, Sep 21 2009
%E A165521 a(0)=1 prepended by _Alois P. Heinz_, Dec 09 2015