A367027 - OEIS

%I #9 Nov 02 2023 10:39:54

%S 1,1,2,4,5,-13,-147,-816,-3534,-12650,-35420,-53040,199056,2391340,

%T 14555740,68264112,261045693,769660569,1167906402,-5145668100,

%U -61758940705,-385813067255,-1857144860445,-7266981925560,-21793022441775,-32643056947527,161919845140752

%N G.f. satisfies A(x) = 1 + x*A(x)^3 - x^2*A(x)^5.

%F 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).

%o (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 Cf. A000108, A137265, A200753, A200755.

%Y Cf. A361245.

%K sign

%O 0,3

%A _Seiichi Manyama_, Nov 02 2023