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 A366221 #17 Mar 03 2024 14:54:16
%S A366221 1,1,5,25,145,905,5941,40433,282721,2018897,14661349,107945993,
%T A366221 803922289,6045458905,45840518933,350100674785,2690717983169,
%U A366221 20794719218593,161502488175557,1259855507859193,9867012143508305,77554946281194793,611575725258403061
%N A366221 G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^2*A(x)^3.
%F A366221 a(n) = Sum_{k=0..n} binomial(2*k,n-k) * binomial(3*k,k)/(2*k+1).
%F A366221 G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A366434.
%t A366221 nmax = 22; A[_] = 1;
%t A366221 Do[A[x_] = 1 + x*(1 + x)^2*A[x]^3 + O[x]^(nmax+1) // Normal, {nmax+1}];
%t A366221 CoefficientList[A[x], x] (* _Jean-François Alcover_, Mar 03 2024 *)
%o A366221 (PARI) a(n) = sum(k=0, n, binomial(2*k, n-k)*binomial(3*k, k)/(2*k+1));
%Y A366221 Cf. A364475, A366200, A366222.
%Y A366221 Cf. A002478, A073155.
%Y A366221 Cf. A366176, A366434.
%K A366221 nonn
%O A366221 0,3
%A A366221 _Seiichi Manyama_, Oct 04 2023