%I #10 Oct 08 2023 10:50:37

%S 1,2,-3,19,-105,690,-4781,34708,-260189,1999169,-15660175,124596499,

%T -1004110947,8179379808,-67239070867,557098881920,-4647368670949,

%U 39001655222788,-329048378867467,2789241880512899,-23743798316713367,202894843070927860

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

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

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

%Y Cf. A007317, A199475, A349289, A349290, A349291, A349292, A349293, A366356, A366358, A366359.

%Y Cf. A364393, A366326, A366364.

%K sign

%O 0,2

%A _Seiichi Manyama_, Oct 08 2023