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 A363431 #14 Sep 01 2023 04:46:04
%S A363431 1,1,1,2,5,14,44,150,496,1758,6018,21782,76414,280448,1001752,3714032,
%T A363431 13450270,50259604,183995056,691863078,2555043320,9657267848,
%U A363431 35921300392,136360740016,510267869416,1944193285228,7312488701868,27950641500876,105590010259396,404724123141348,1534775681029994
%N A363431 Number of 123-avoiding stabilized-interval-free permutations of size n.
%C A363431 A stabilized-interval-free (SIF) permutation on [n] = {1, 2, ..., n} is one that does not stabilize any proper subinterval of [n].
%H A363431 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 A363431 For n>2, a(n) = f_0(n) - f_1(n-1) + f_2(n) - Sum_{k=1..floor((n-3)/2)} C(k)^2*a(n-2*k), where C(k)=binomial(2*k,k)/(k+1) and f_j(m) denotes the number of 123-avoiding permutations of size m having j fixed points.
%e A363431 For n=4 the a(4)=5 permutations are 2413, 3142, 3412, 3421, 4312.
%Y A363431 Cf. A075834.
%K A363431 nonn
%O A363431 0,4
%A A363431 _Juan B. Gil_, Jun 22 2023