%I #9 Mar 27 2024 08:53:43
%S 1,3,9,34,141,621,2849,13467,65127,320686,1602294,8103087,41397186,
%T 213331026,1107604764,5788249329,30422897664,160717169622,
%U 852894534042,4544635033164,24305345593290,130423538829518,701994030831654,3788979493701069,20503322609731348
%N G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^3.
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(3*k+3,k)/(k+1).
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(3*k+3, k)/(k+1));
%Y Cf. A127897, A370720, A371494.
%Y Cf. A371516.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 26 2024