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 A364595 #9 Jul 29 2023 10:50:46 %S A364595 1,1,1,2,3,4,8,15,25,50,102,193,390,815,1645,3385,7141,14893,31196, %T A364595 66309,140752,299043,640367,1373929,2950006,6360976,13749865,29753891, %U A364595 64547097,140329453,305470485,666084272,1454920255,3181946080,6968134645,15280422274 %N A364595 G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^3. %F A364595 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(3*k,k) / (2*k+1). %o A364595 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(3*k, k)/(2*k+1)); %Y A364595 Cf. A364596, A364597. %K A364595 nonn,easy %O A364595 0,4 %A A364595 _Seiichi Manyama_, Jul 29 2023