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 A360050 #13 Jan 25 2023 08:40:18
%S A360050 1,4,10,20,34,48,48,0,-163,-548,-1274,-2340,-3255,-2224,5304,28560,
%T A360050 82379,182300,322102,410700,133128,-1295264,-5440600,-14733680,
%U A360050 -31384533,-52870668,-59633454,11449780,312532426,1137823168,2918752832,5961965824,9464314955
%N A360050 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+3,4*k+3) * Catalan(k).
%F A360050 a(n) = binomial(n+3,3) - Sum_{k=0..n-4} a(k) * a(n-k-4).
%F A360050 G.f. A(x) satisfies: A(x) = 1/(1-x)^4 - x^4 * A(x)^2.
%F A360050 G.f.: 2 / ( (1-x)^2 * ((1-x)^2 + sqrt((1-x)^4 + 4*x^4)) ).
%F A360050 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) +(9*n-8)*a(n-4) +5*(-n+1)*a(n-5) =0. - _R. J. Mathar_, Jan 25 2023
%o A360050 (PARI) a(n) = sum(k=0, n\4, (-1)^k*binomial(n+3, 4*k+3)*binomial(2*k, k)/(k+1));
%o A360050 (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 A360050 Cf. A360048, A360049, A360051.
%Y A360050 Cf. A000108.
%K A360050 sign
%O A360050 0,2
%A A360050 _Seiichi Manyama_, Jan 23 2023