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 A360076 #28 Jan 25 2023 09:08:17
%S A360076 1,1,5,20,90,430,2136,10937,57307,305822,1656482,9083432,50328114,
%T A360076 281324294,1584578746,8984740485,51242962251,293772468164,
%U A360076 1691974930584,9785378133297,56805049768157,330880419984832,1933299689139364,11328101469158554
%N A360076 a(n) = Sum_{k=0..n} binomial(3*k,n-k) * Catalan(k).
%F A360076 G.f. A(x) satisfies A(x) = 1/(1 - x * (1+x)^3 * A(x)).
%F A360076 G.f.: 2 / (1 + sqrt( 1 - 4*x*(1+x)^3 )).
%o A360076 (PARI) a(n) = sum(k=0, n, binomial(3*k, n-k)*binomial(2*k, k)/(k+1));
%o A360076 (PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+x)^3)))
%Y A360076 Cf. A052709, A073155, A360082, A360083.
%Y A360076 Cf. A000108, A099234.
%K A360076 nonn
%O A360076 0,3
%A A360076 _Seiichi Manyama_, Jan 25 2023