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%I #9 Sep 16 2023 10:42:10
%S 1,1,1,2,8,30,103,368,1407,5531,21905,87689,355929,1461022,6046160,
%T 25194331,105661615,445692621,1889454880,8045796200,34398989998,
%U 147606568810,635481458969,2744158752772,11882687400375,51584960268914,224465280616995,978851595046223
%N G.f. satisfies A(x) = 1 + x*A(x) / (1 - x^2*A(x)^5).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1,k) * binomial(n+3*k+1,n-2*k) / (n+3*k+1).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n-k-1, k)*binomial(n+3*k+1, n-2*k)/(n+3*k+1));
%Y Cf. A101785, A365244, A365692.
%Y Cf. A365691.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 16 2023
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