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 A366588 #18 Oct 14 2024 23:59:39
%S A366588 1,0,0,1,1,0,2,4,2,5,15,15,19,56,84,98,224,420,552,1002,2022,3069,
%T A366588 4983,9801,16577,26455,49049,87945,144287,255112,465244,792012,
%U A366588 1369862,2482714,4348838,7509580,13439724,23911044,41643744,73832632,132039816,232391394
%N A366588 G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)*A(x)^2.
%H A366588 Robert Israel, <a href="/A366588/b366588.txt">Table of n, a(n) for n = 0..3794</a>
%F A366588 G.f.: A(x) = 2 / (1+sqrt(1-4*x^3*(1+x))).
%F A366588 a(n) = Sum_{k=0..floor(n/3)} binomial(k,n-3*k) * binomial(2*k,k)/(k+1).
%F A366588 (4*n + 8)*a(n) + (22 + 8*n)*a(n + 1) + (14 + 4*n)*a(n + 2) + (-8 - n)*a(n + 4) + (-8 - n)*a(n + 5) = 0. - _Robert Israel_, Oct 14 2024
%p A366588 f:= gfun:-rectoproc({(4*n + 8)*a(n) + (22 + 8*n)*a(n + 1) + (14 + 4*n)*a(n + 2) + (-8 - n)*a(n + 4) + (-8 - n)*a(n + 5) = 0,a(0)=1,a(1)=0,a(2)=0,a(3)=1,a(4)=1}, a(n),remember):
%p A366588 map(f, [$0..30]); # _Robert Israel_, Oct 14 2024
%o A366588 (PARI) a(n) = sum(k=0, n\3, binomial(k, n-3*k)*binomial(2*k, k)/(k+1));
%Y A366588 Cf. A115178, A366589.
%Y A366588 Cf. A248100.
%K A366588 nonn
%O A366588 0,7
%A A366588 _Seiichi Manyama_, Oct 14 2023