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 A023422 #34 Feb 03 2025 09:35:37
%S A023422 1,1,1,1,1,1,2,4,8,16,32,64,129,261,530,1080,2208,4528,9313,19207,
%T A023422 39714,82314,170996,355976,742545,1551817,3248823,6812947,14309557,
%U A023422 30099645,63402315
%N A023422 Generalized Catalan Numbers x^2*A(x)^2 -(1-x+x^2+x^3+x^4+x^5)*A(x) + 1 =0.
%H A023422 Seiichi Manyama, <a href="/A023422/b023422.txt">Table of n, a(n) for n = 0..2926</a>
%H A023422 A. Goupil, M.-E. Pellerin and J. de Wouters d'oplinter, <a href="http://arxiv.org/abs/1307.8432">Snake Polyominoes</a>, arXiv preprint arXiv:1307.8432 [math.CO], 2013-2014. (Gives a g.f.)
%F A023422 G.f. A(x) satisfies: A(x) = (1 + x^2 * A(x)^2) / (1 - x + x^2 + x^3 + x^4 + x^5). - _Ilya Gutkovskiy_, Jul 20 2021
%F A023422 D-finite with recurrence (n+2)*a(n) +(-2*n-1)*a(n-1) +(-n+1)*a(n-2) +(n-4)*a(n-4) +(2*n-11)*a(n-5) +(n-7)*a(n-6) +2*(2*n-17)*a(n-7) +3*(n-10)*a(n-8) +(2*n-23)*a(n-9) +(n-13)*a(n-10)=0. - _R. J. Mathar_, Feb 03 2025
%t A023422 a[0]=1; a[n_]:= a[n]=a[n-1] + Sum[a[k]*a[n-2-k], {k,4,n-2}]; Table[a[n], {n,0,30}] (* modified by _G. C. Greubel_, Jan 01 2018 *)
%t A023422 B[q_] = (q^2 + q^3 + q^4 + q^5 - Sqrt[((q(q^5 - 1))/(q - 1) - 1)^2 - 4q^6] - q + 1)/(2q^2); CoefficientList[B[q] + O[q]^31, q] (* _Jean-François Alcover_, Jan 29 2019 *)
%o A023422 (PARI) {a(n) = if(n==0,1, a(n-1) + sum(k=4,n-2, a(k)*a(n-k-2)))};
%o A023422 for(n=0,30, print1(a(n), ", ")) \\ _G. C. Greubel_, Jan 01 2018
%Y A023422 Cf. A000108, A001006, A004148, A004149, A023421, A023423.
%Y A023422 Fifth row of A064645.
%K A023422 nonn,easy
%O A023422 0,7
%A A023422 _Olivier Gérard_