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 A367027 #13 Mar 08 2025 09:32:15
%S A367027 1,1,2,4,5,-13,-147,-816,-3534,-12650,-35420,-53040,199056,2391340,
%T A367027 14555740,68264112,261045693,769660569,1167906402,-5145668100,
%U A367027 -61758940705,-385813067255,-1857144860445,-7266981925560,-21793022441775,-32643056947527,161919845140752
%N A367027 G.f. A(x) satisfies A(x) = 1 + x*A(x)^3 - x^2*A(x)^5.
%F A367027 a(n) = (1/(2*n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n-k,k) * binomial(3*n-2*k,n-2*k).
%F A367027 G.f.: ( (1/x) * Series_Reversion( x * (1-x+x^2)^2 ) )^(1/2). - _Seiichi Manyama_, Mar 08 2025
%o A367027 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(3*n-k, k)*binomial(3*n-2*k, n-2*k))/(2*n+1);
%Y A367027 Cf. A000108, A137265, A200753, A200755.
%Y A367027 Cf. A361245, A368969.
%K A367027 sign
%O A367027 0,3
%A A367027 _Seiichi Manyama_, Nov 02 2023