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 A360082 #8 Jan 25 2023 09:08:13
%S A360082 1,1,6,27,134,709,3892,22004,127250,749230,4476386,27071344,165398868,
%T A360082 1019405720,6330482488,39571612357,248796862550,1572300095758,
%U A360082 9981970108384,63633339713190,407162295120570,2614059813642256,16834457481559076
%N A360082 a(n) = Sum_{k=0..n} binomial(4*k,n-k) * Catalan(k).
%F A360082 G.f. A(x) satisfies A(x) = 1/(1 - x * (1+x)^4 * A(x)).
%F A360082 G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^4 )).
%o A360082 (PARI) a(n) = sum(k=0, n, binomial(4*k, n-k)*binomial(2*k, k)/(k+1));
%o A360082 (PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+x)^4)))
%Y A360082 Cf. A052709, A073155, A360076, A360083.
%Y A360082 Cf. A000108, A099235.
%K A360082 nonn
%O A360082 0,3
%A A360082 _Seiichi Manyama_, Jan 25 2023