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 A364161 #21 Aug 29 2023 05:09:51
%S A364161 1,1,2,5,15,47,153,514,1769,6205,22102,79733,290721,1069688,3966739,
%T A364161 14810348,55627778,210046102,796864028,3035912900,11610468138,
%U A364161 44556451207,171529074168,662238211929,2563524741603,9947573055828,38687704042595
%N A364161 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)).
%F A364161 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(2*n-5*k+1,n-3*k)/(2*n-5*k+1).
%F A364161 D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(n+1)*a(n-2) +3*(-2*n+3)*a(n-3) +(-2*n+7)*a(n-5) +(n-8)*a(n-6) +(n-8)*a(n-8)=0. - _R. J. Mathar_, Aug 29 2023
%p A364161 A364161 := proc(n)
%p A364161 add( binomial(n-2*k-1,k)*binomial(2*n-5*k+1,n-3*k)/(2*n5*k+1),k=0..floor(n/3)) ;
%p A364161 end proc:
%p A364161 seq(A364161(n),n=0..80); # _R. J. Mathar_, Aug 29 2023
%o A364161 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-5*k+1, n-3*k)/(2*n-5*k+1));
%Y A364161 Cf. A001003, A119370.
%Y A364161 Cf. A218251, A364833, A365247.
%K A364161 nonn
%O A364161 0,3
%A A364161 _Seiichi Manyama_, Aug 28 2023