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 A360046 #17 Jan 25 2023 08:32:05
%S A360046 1,4,10,20,36,64,120,240,497,1036,2158,4524,9625,20816,45560,100368,
%T A360046 221915,492380,1097302,2457228,5526666,12474000,28233600,64061920,
%U A360046 145704327,332174532,758977386,1737703780,3985847284,9157908736,21074460512,48569746368,112096071675
%N A360046 a(n) = Sum_{k=0..floor(n/4)} binomial(n+3,4*k+3) * Catalan(k).
%H A360046 Seiichi Manyama, <a href="/A360046/b360046.txt">Table of n, a(n) for n = 0..1000</a>
%F A360046 a(n) = binomial(n+3,3) + Sum_{k=0..n-4} a(k) * a(n-k-4).
%F A360046 G.f. A(x) satisfies: A(x) = 1/(1-x)^4 + x^4 * A(x)^2.
%F A360046 G.f.: 2 / ( (1-x)^2 * ((1-x)^2 + sqrt((1-x)^4 - 4*x^4)) ).
%F A360046 D-finite with recurrence (n+4)*a(n) +5*(-n-3)*a(n-1) +10*(n+2)*a(n-2) +10*(-n-1)*a(n-3) +(n+8)*a(n-4) +3*(n-1)*a(n-5)=0. - _R. J. Mathar_, Jan 25 2023
%o A360046 (PARI) a(n) = sum(k=0, n\4, binomial(n+3, 4*k+3)*binomial(2*k, k)/(k+1));
%o A360046 (PARI) my(N=40, x='x+O('x^N)); Vec(2/((1-x)^2*((1-x)^2+sqrt((1-x)^4-4*x^4))))
%Y A360046 Cf. A086615, A360045, A360047.
%Y A360046 Cf. A000108.
%K A360046 nonn
%O A360046 0,2
%A A360046 _Seiichi Manyama_, Jan 23 2023