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 A367640 #11 Dec 04 2023 05:01:18
%S A367640 1,3,8,36,200,1220,7896,53220,369528,2624772,18981864,139287588,
%T A367640 1034475624,7761249476,58735359032,447827171556,3436759851672,
%U A367640 26526255859716,205782644595912,1603655203428900,12548225647402248,98548826076070596,776552629964300952
%N A367640 G.f. A(x) satisfies A(x) = (1 + x)^2 + x*A(x)^3 / (1 + x)^2.
%F A367640 a(n) = Sum_{k=0..n} binomial(2*k+2,n-k) * binomial(3*k,k)/(2*k+1).
%F A367640 D-finite with recurrence 2*n*(14*n+71)*(2*n+1)*a(n) +3*(-150*n^3-209*n^2-379*n+228)*a(n-1) +9*(-30*n^3-981*n^2+4297*n-3624)*a(n-2) +27*(n-4)*(22*n^2-491*n+1151)*a(n-3) +81*(n-4)*(n-5)*(6*n-49)*a(n-4)=0. - _R. J. Mathar_, Dec 04 2023
%o A367640 (PARI) a(n) = sum(k=0, n, binomial(2*k+2, n-k)*binomial(3*k, k)/(2*k+1));
%Y A367640 Cf. A367639, A367641.
%Y A367640 Cf. A366221, A366266.
%K A367640 nonn
%O A367640 0,2
%A A367640 _Seiichi Manyama_, Nov 25 2023