%I #11 Oct 10 2023 05:09:24

%S 1,1,-4,16,-84,496,-3140,20832,-142932,1005856,-7220100,52657392,

%T -389088084,2906551440,-21914464708,166548194240,-1274531623764,

%U 9812792232768,-75955668337412,590742300208848,-4614140648464980,36178872976542768,-284664427193774916

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

%F a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(3*k-1,k) * binomial(2*k,n-k) / (3*k-1).

%o (PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(2*k, n-k)/(3*k-1));

%Y Partial sums give A366364.

%Y Cf. A366431, A366432, A366433, A366435, A366436, A366437.

%K sign

%O 0,3

%A _Seiichi Manyama_, Oct 09 2023