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 A365247 #10 Aug 28 2023 10:51:59
%S A365247 1,1,2,5,15,50,177,650,2449,9412,36761,145518,582556,2354557,9594898,
%T A365247 39378259,162619316,675258452,2817643240,11808576745,49683880754,
%U A365247 209786559004,888676860191,3775654643360,16084818268474,68694452578325,294053067958011
%N A365247 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)^4).
%F A365247 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(2*n-2*k+1,n-3*k)/(2*n-2*k+1).
%o A365247 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-2*k+1, n-3*k)/(2*n-2*k+1));
%Y A365247 Cf. A364739, A365246.
%Y A365247 Cf. A218251, A364161, A364833.
%K A365247 nonn
%O A365247 0,3
%A A365247 _Seiichi Manyama_, Aug 28 2023