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 A343795 #19 May 04 2021 18:09:25
%S A343795 1,1,3,10,39,174,872,4805,28474,178099,1160173,7803860,53924841,
%T A343795 381640934,2761331130,20400560942,153738854242,1180631743440,
%U A343795 9229687049249,73372263658451,592476077260123,4854377724124700,40315729803287046,339065862485375334,2885324166565733641
%N A343795 Number of Dumont permutations of the fourth kind of length 2n avoiding the pattern 312.
%C A343795 Dumont permutations of the fourth kind are permutations of even length where all deficiencies (drops) are even values at even positions.
%D A343795 O. Jones, Enumeration of Dumont permutations avoiding certain four-letter patterns, Ph.D. thesis, Howard University, 2019.
%H A343795 A. Burstein and O. Jones, <a href="https://arxiv.org/abs/2002.12189">Enumeration of Dumont permutations avoiding certain four-letter patterns</a>, arXiv:2002.12189 [math.CO], 2020.
%H A343795 A. Burstein, M. Josuat-Vergès, and W. Stromquist, <a href="http://puma.dimai.unifi.it/21_2/5_Burstein_Josuat-Verges_Stromquist.pdf">New Dumont permutations</a>, Pure Math. Appl. (Pu.M.A.) 21 (2010), no. 2, 177-206.
%F A343795 Let F_k(x) be the truncation of the g.f. of A048990 to a polynomial of degree k. Let G_k(x) be the truncation of the g.f. of A024492 to a polynomial of degree k. Let G_{-1}(x) = 0. For k>=0, define A_k(x) recursively as follows: A_k(x) = F_k(x)/((1-x*G_{k-1}(x))^2-x*F_k(x)/(1-x*G_k(x)-x*F_k(x)^2/(1-x*A_{k+1}(x)))). Then A_0(x) is the g.f. of this sequence.
%e A343795 For n=2, a(2)=3 counts the permutations 1234, 1342, 1432.
%o A343795 (PARI) seq(n)={my(h=sqrt(1-16*x + O(x*x^n)), F=sqrt((1-h)/(8*x)), G=(1-sqrt((1+h)/2))/(2*x), A=O(1)); forstep(k=n\3, 0, -1, my(f=Pol(F + O(x*x^k))); A = f/((1 - x*Pol(G + O(x^k)))^2 - x*f/(1 - x*Pol(G + O(x*x^k)) - x*f^2/(1 - x*A))) ); Vec(A + O(x*x^n))} \\ _Andrew Howroyd_, Apr 29 2021
%Y A343795 Cf. A000108 (permutations avoiding 312), A024492, A048990, A110501 (length 2n Dumont permutations of 4th kind).
%K A343795 easy,nonn
%O A343795 0,3
%A A343795 _Alexander Burstein_ and _Opel Jones_, Apr 29 2021
%E A343795 Terms a(12) and beyond from _Andrew Howroyd_, Apr 29 2021