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%I #26 Aug 06 2023 11:04:41
%S 1,1,1,-3,-21,-41,166,1460,3445,-13503,-136721,-364412,1285021,
%T 14694643,43144726,-132548857,-1709480698,-5456400119,14285376285,
%U 209281385564,720201663662,-1572818128366,-26541960203077,-97918748134874,173825501585400,3453517916428141
%N G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 + x*A(x)^5).
%F a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(2*n+3*k,n-1-k) for n > 0.
%o (PARI) a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(2*n+3*k, n-1-k))/n);
%Y Cf. A291534, A363982, A364764.
%Y Cf. A364740.
%K sign
%O 0,4
%A _Seiichi Manyama_, Aug 05 2023