%I #9 Oct 08 2023 10:50:32
%S 1,2,-2,14,-70,426,-2714,18118,-124814,881042,-6339058,46318334,
%T -342769750,2563781690,-19350683018,147197511222,-1127334112542,
%U 8685458120226,-67270210217186,523472089991662,-4090668558473318,32088204418069450,-252576222775705466
%N G.f. satisfies A(x) = (1 + x/A(x)^2)/(1 - x).
%F a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(3*k-1,k) * binomial(2*k-1,n-k)/(3*k-1).
%o (PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(2*k-1, n-k)/(3*k-1));
%Y Cf. A346626, A349310, A349311, A349312, A349313, A349314, A366363, A366365, A366366.
%Y Cf. A366357.
%K sign
%O 0,2
%A _Seiichi Manyama_, Oct 08 2023