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 A360027 #24 Jan 25 2023 08:27:44
%S A360027 1,1,1,1,1,0,-1,-2,-3,-4,-3,0,5,12,21,27,25,10,-23,-79,-149,-210,-225,
%T A360027 -143,101,544,1153,1783,2135,1714,-81,-3735,-9263,-15724,-20603,
%U A360027 -19490,-6485,24242,75307,140955,200891,215530,126527,-132122,-605687
%N A360027 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * binomial(n-4*k,k) * Catalan(k).
%H A360027 Seiichi Manyama, <a href="/A360027/b360027.txt">Table of n, a(n) for n = 0..1000</a>
%F A360027 a(n) = 1 - Sum_{k=0..n-5} a(k) * a(n-k-5).
%F A360027 G.f. A(x) satisfies: A(x) = 1/(1-x) - x^5 * A(x)^2.
%F A360027 G.f.: 2 / ( 1-x + sqrt((1-x)^2 + 4*x^5*(1-x)) ).
%F A360027 D-finite with recurrence (n+5)*a(n) 2*(-n-4)*a(n-1) +(n+3)*a(n-2) +2*(2*n-5)*a(n-5) +4*(-n+3)*a(n-6)=0. - _R. J. Mathar_, Jan 25 2023
%o A360027 (PARI) a(n) = sum(k=0, n\5, (-1)^k*binomial(n-4*k, k)*binomial(2*k, k)/(k+1));
%o A360027 (PARI) my(N=50, x='x+O('x^N)); Vec(2/(1-x+sqrt((1-x)^2+4*x^5*(1-x))))
%Y A360027 Cf. A360024, A360025, A360026.
%Y A360027 Cf. A000108, A346074.
%K A360027 sign
%O A360027 0,8
%A A360027 _Seiichi Manyama_, Jan 22 2023