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 A367237 #11 Nov 13 2023 11:33:16
%S A367237 1,1,4,20,114,702,4550,30585,211270,1490561,10695354,77809481,
%T A367237 572608270,4254996670,31882486314,240620654468,1827464108766,
%U A367237 13956516915303,107114560278680,825727777034002,6390721805005678,49638977802126104,386824024893533450
%N A367237 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^2)^2.
%F A367237 If g.f. satisfies A(x) = 1 + x*A(x)^t / (1 - x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(n+(s-1)*k-1,n-k) / (t*k+u*(n-k)+1).
%F A367237 a(n) ~ sqrt((12735 + (849*(23867603343 - 274945024*sqrt(849)))^(1/3) + (849*(23867603343 + 274945024*sqrt(849)))^(1/3))/283) * ((2053 + (10379182717 - 43903488*sqrt(849))^(1/3) + (10379182717 + 43903488*sqrt(849))^(1/3))^n / (sqrt(Pi) * n^(3/2) * 2^(8*n + 9/2) * 3^(n + 1/2))). - _Vaclav Kotesovec_, Nov 13 2023
%t A367237 CoefficientList[Series[Root[-1 + #1 + x*#1^2 - 2*x*#1^3 - x^2*#1^4 + x^2*#1^5&, 1],{x,0,20}],x] (* _Vaclav Kotesovec_, Nov 13 2023 *)
%o A367237 (PARI) a(n, s=2, t=2, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
%Y A367237 Cf. A001764, A367236, A367238.
%K A367237 nonn
%O A367237 0,3
%A A367237 _Seiichi Manyama_, Nov 11 2023