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%I #11 Nov 03 2023 11:20:20
%S 1,1,2,9,40,192,963,5000,26649,144990,802023,4497150,25504380,
%T 146037955,843134220,4902661503,28686940053,168785282241,997968554037,
%U 5926617173205,35335723342962,211433954924955,1269252184538408,7642065274626855,46137678521488140
%N G.f. satisfies A(x) = 1 - x^2 + x*A(x)^3.
%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*(n-2*k)+1,k) * binomial(3*(n-2*k),n-2*k)/(2*(n-2*k)+1).
%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(2*(n-2*k)+1, k)*binomial(3*(n-2*k), n-2*k)/(2*(n-2*k)+1));
%Y Cf. A025262, A367045.
%Y Cf. A367040.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 03 2023
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