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 A361488 #30 Mar 23 2023 07:57:15
%S A361488 1,0,0,2,2,0,6,12,6,20,60,60,90,280,420,532,1330,2520,3444,6804,14112,
%T A361488 21912,37884,77616,133914,223080,432432,793364,1341912,2471040,
%U A361488 4629196,8076640,14453010,26960232,48308832,85794852,157947816,287413152,512697900,933072064
%N A361488 Diagonal of rational function 1/(1 - (x^3 + y^3 + x^4*y)).
%H A361488 Seiichi Manyama, <a href="/A361488/b361488.txt">Table of n, a(n) for n = 0..1000</a>
%F A361488 G.f.: 1/sqrt(1 - 4 * x^3 * (1+x)).
%F A361488 a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,k) * binomial(k,n-3*k).
%F A361488 From _Vaclav Kotesovec_, Mar 23 2023: (Start)
%F A361488 Recurrence: n*a(n) = 2*(2*n-3)*a(n-3) + 4*(n-2)*a(n-4).
%F A361488 a(n) ~ sqrt(c) * d^n / sqrt(Pi*n), where d = 1.835086681639635368143322042736678753... is the positive real root of the equation d^4 - 4*d - 4 = 0 and c = 0.2982650309662120181812121016104223... is the largest real root of the equation 1 - 20*c + 132*c^2 - 364*c^3 + 364*c^4 = 0. (End)
%t A361488 Table[Sum[Binomial[2*k,k] * Binomial[k,n-3*k], {k,0,n/3}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 23 2023 *)
%o A361488 (PARI) a(n) = sum(k=0, n\3, binomial(2*k, k)*binomial(k, n-3*k));
%Y A361488 Cf. A006139, A115962.
%Y A361488 Cf. A360267, A361727.
%K A361488 nonn
%O A361488 0,4
%A A361488 _Seiichi Manyama_, Mar 22 2023