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%I #8 Oct 04 2023 12:51:01
%S 1,1,8,60,520,4886,48384,497460,5259872,56834345,624819148,6966612604,
%T 78592083420,895432704860,10288759392156,119089472755860,
%U 1387274092156508,16251727492295812,191342076640423136,2262894045516407118,26869820052175649836
%N G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^4*A(x)^4.
%F a(n) = Sum_{k=0..n} binomial(4*k,n-k) * binomial(4*k,k)/(3*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(4*k, n-k)*binomial(4*k, k)/(3*k+1));
%Y Cf. A073155, A366200.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 04 2023