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 A376574 #18 Oct 24 2024 04:56:28
%S A376574 1,1,2,5,15,46,147,486,1646,5684,19940,70864,254592,923153,3374046,
%T A376574 12417246,45975677,171141378,640105278,2404375805,9066188052,
%U A376574 34305301482,130219435385,495735347502,1892254721982,7240580768021,27768359445128,106718055778871
%N A376574 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)/(1 - x^3)).
%F A376574 a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * Catalan(n-3*k).
%F A376574 G.f.: 2/(1 + sqrt(1 - 4*x/(1 - x^3))).
%F A376574 D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(-2*n+7)*a(n-3) +4*(n-5)*a(n-4) +(n-8)*a(n-6)=0. - _R. J. Mathar_, Oct 24 2024
%p A376574 A376574 := proc(n)
%p A376574 add(A000108(n-3*k)*binomial(n-2*k-1,k),k=0..floor(n/3)) ;
%p A376574 end proc:
%p A376574 seq(A376574(n),n=0..80) ;
%p A376574 # _R. J. Mathar_, Oct 24 2024
%o A376574 (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*(n-3*k), n-3*k)/(n-3*k+1));
%o A376574 (PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x/(1-x^3))))
%Y A376574 Cf. A002212, A085139.
%Y A376574 Cf. A000108, A360272.
%K A376574 nonn
%O A376574 0,3
%A A376574 _Seiichi Manyama_, Sep 28 2024