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 A363432 #10 Jul 29 2023 03:18:37
%S A363432 1,1,1,1,2,6,18,54,170,551,1817,6092,20722,71325,248055,870402,
%T A363432 3077861,10959008,39261382,141430953,512002865,1861872379,6798330676,
%U A363432 24915934639,91630864177,338048560865,1250793108398,4640542045919,17260221009367,64349394615738,240434325753052
%N A363432 Number of 231-avoiding stabilized-interval-free permutations of size n.
%C A363432 A stabilized-interval-free (SIF) permutation on [n] = {1, 2, ..., n} is one that does not stabilize any proper subinterval of [n].
%C A363432 a(n) is also the number of 312-avoiding SIF permutations of size n.
%H A363432 Daniel Birmajer, Juan B. Gil, Jordan O. Tirrell, and Michael D. Weiner, <a href="https://arxiv.org/abs/2306.03155">Pattern-avoiding stabilized-interval-free permutations</a>, arXiv:2306.03155 [math.CO], 2023.
%F A363432 G.f.: 1 + x/(1+C(1)*x^2*(x+1)-x/(1+C(2)*x^3*(x+1)-x/(1+C(3)*x^4*(x+1)-x/(...)))), where C(k)=binomial(2*k,k)/(k+1).
%e A363432 For n=5 the a(5)=6 permutations are 51234, 51423, 53124, 54123, 54132, 54213.
%t A363432 nmax = 30; CoefficientList[Series[1 + x/(1 + CatalanNumber[1]*x^2*(x + 1) + ContinuedFractionK[-x, 1 + CatalanNumber[k]*x^(k + 1)*(x + 1), {k, 2, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 23 2023 *)
%Y A363432 Cf. A000108, A075834.
%K A363432 nonn
%O A363432 0,5
%A A363432 _Juan B. Gil_, Jun 22 2023