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G.f. A(x) satisfies A(x) = 1 + x*(1 + x)^4*A(x)^4.
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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