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 A364475 #13 Nov 23 2024 11:10:51
%S A364475 1,1,4,18,94,529,3135,19270,121732,785496,5155167,34304706,230923653,
%T A364475 1569684910,10759159000,74281473504,516089542684,3605685460750,
%U A364475 25316226436086,178538289189108,1264131169628799,8982889404251721,64041351551534215
%N A364475 G.f. satisfies A(x) = 1 + x*A(x)^3 + x^2*A(x)^3.
%F A364475 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-3*k,k) * binomial(3*n-4*k,n-2*k) / (2*n-2*k+1).
%F A364475 D-finite with recurrence 2*n*(2*n+1)*a(n) -(5*n+1)*(3*n-2)*a(n-1) +4*(-25*n^2+75*n-59) *a(n-2) +9*(-15*n^2+69*n-80)*a(n-3) -6*(3*n-8)*(3*n-10) *a(n-4)=0. - _R. J. Mathar_, Jul 27 2023
%p A364475 A364475 := proc(n)
%p A364475 add( binomial(3*n-3*k,k) * binomial(3*n-4*k,n-2*k)/(2*n-2*k+1),k=0..n/2) ;
%p A364475 end proc:
%p A364475 seq(A364475(n),n=0..80); # _R. J. Mathar_, Jul 27 2023
%o A364475 (PARI) a(n) = sum(k=0, n\2, binomial(3*n-3*k, k)*binomial(3*n-4*k, n-2*k)/(2*n-2*k+1));
%Y A364475 Column k=1 of A378323.
%Y A364475 Cf. A002293, A104979, A186997, A255673, A361245, A364474, A364478.
%K A364475 nonn
%O A364475 0,3
%A A364475 _Seiichi Manyama_, Jul 26 2023