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 A360048 #12 Jan 25 2023 08:36:30
%S A360048 1,2,2,0,-3,-2,9,24,11,-66,-152,-8,587,1082,-438,-5248,-7733,7942,
%T A360048 47502,53792,-105313,-430118,-343043,1249800,3866557,1730018,
%U A360048 -13996096,-34243896,-1947203,150962374,296101865,-121857184,-1582561869,-2468098042,2529520766
%N A360048 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n+1,2*k+1) * Catalan(k).
%F A360048 a(n) = n+1 - Sum_{k=0..n-2} a(k) * a(n-k-2).
%F A360048 G.f. A(x) satisfies: A(x) = 1/(1-x)^2 - x^2 * A(x)^2.
%F A360048 G.f.: 2 / ( (1-x) * (1-x + sqrt((1-x)^2 + 4*x^2)) ).
%F A360048 D-finite with recurrence (n+2)*a(n) +3*(-n-1)*a(n-1) +(7*n-4)*a(n-2) +5*(-n+1)*a(n-3)=0. - _R. J. Mathar_, Jan 25 2023
%o A360048 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n+1, 2*k+1)*binomial(2*k, k)/(k+1));
%o A360048 (PARI) my(N=40, x='x+O('x^N)); Vec(2/((1-x)*(1-x+sqrt((1-x)^2+4*x^2))))
%Y A360048 Cf. A360049, A360050, A360051.
%Y A360048 Cf. A000108.
%K A360048 sign
%O A360048 0,2
%A A360048 _Seiichi Manyama_, Jan 23 2023