%I #95 Oct 23 2024 09:27:21
%S 1,3,9,18,0,-162,-567,0,8019,31590,0,-520506,-2160756,0,38480265,
%T 164549880,0,-3072083274,-13390246485,0,258054995016,1139882486490,0,
%U -22474826957232,-100257845970825,0,2011064804461548,9039247392729582,0,-183769714890451800
%N G.f. satisfies A(x) = (1 + 9*x*A(x)^2)^(1/3).
%F a(n) = 9^n * binomial(2*n/3 + 1/3,n)/(2*n+1).
%o (PARI) a(n) = 9^n*binomial(2*n/3+1/3, n)/(2*n+1);
%Y Cf. A004987, A008931, A078532, A245114, A376282.
%K sign,new
%O 0,2
%A _Seiichi Manyama_, Oct 23 2024