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%I #22 Aug 07 2023 07:46:06
%S 1,1,2,8,38,196,1073,6120,35968,216304,1324676,8232981,51796538,
%T 329229344,2111031444,13638557196,88695018723,580153216512,
%U 3814285704000,25192499164320,167075960048996,1112162062296061,7428213584196010,49766086788057256
%N G.f. satisfies A(x) = 1 + x*A(x) / (1 - x*A(x)^4).
%F a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(n+3*k,n-1-k) for n > 0.
%o (PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(n+3*k, n-1-k))/n);
%Y Cf. A000108, A106228, A300048, A364734.
%Y Cf. A364739.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 05 2023