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 A322189 #7 Dec 07 2018 22:52:10
%S A322189 1,3,72,2208,75531,2748957,104125542,4055630148,161248468944,
%T A322189 6513248563281,266402605165194,11007646816287168,458676184166135532,
%U A322189 19248392999470239126,812657808793768897362,34489498873811554580556,1470421670132406007539195,62941195430565633995463225,2703764557673857477236184014,116513978125127785773539029596
%N A322189 G.f. A(x) satisfies: A(x)^2 + A(x) - 1 = Sum_{n>=0} binomial(3*n,n)^2 * x^n.
%C A322189 Radius of convergence of g.f. A(x) is r = 2^4/3^6 = 16/729.
%e A322189 G.f.: A(x) = 1 + 3*x + 72*x^2 + 2208*x^3 + 75531*x^4 + 2748957*x^5 + 104125542*x^6 + 4055630148*x^7 + 161248468944*x^8 + 6513248563281*x^9 + ...
%e A322189 such that
%e A322189 A(x)^2 + A(x) - 1 = 1 + 9*x + 225*x^2 + 7056*x^3 + 245025*x^4 + 9018009*x^5 + 344622096*x^6 + 13521038400*x^7 + 540917591841*x^8 + 21966328580625*x^9 + ... + binomial(3*n,n)^2 * x^n + ...
%o A322189 (PARI) {S(n) = sum(m=0,n, binomial(3*m,m)^2 * x^m ) +x*O(x^n)}
%o A322189 {A(n) = (sqrt(4*S(n) + 5) - 1)/2 }
%o A322189 {a(n) = polcoeff( A(n), n)}
%o A322189 for(n=0,30, print1(a(n),", "))
%Y A322189 Cf. A188662.
%K A322189 nonn
%O A322189 0,2
%A A322189 _Paul D. Hanna_, Dec 07 2018