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 A365223 #8 Aug 27 2023 04:38:02
%S A365223 1,1,2,3,-3,-50,-244,-714,-530,8522,63548,259473,535647,-1321437,
%T A365223 -19094684,-103022071,-322370363,-142186810,5537336460,41081448638,
%U A365223 170484444654,332739198585,-1241023311708,-15677607031084,-83737193010368,-255608722098225,-12706843586158
%N A365223 G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^4).
%F A365223 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(4*n-k+1,k) * binomial(n-1,n-k)/(4*n-k+1).
%o A365223 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(4*n-k+1, k)*binomial(n-1, n-k)/(4*n-k+1));
%Y A365223 Cf. A000108, A106228, A127897, A364864.
%Y A365223 Cf. A365224, A365226.
%K A365223 sign
%O A365223 0,3
%A A365223 _Seiichi Manyama_, Aug 27 2023