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G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^4.
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%I #11 Jul 29 2023 10:52:49

%S 1,1,2,4,11,31,98,316,1065,3649,12775,45299,162713,590097,2159015,

%T 7957003,29517141,110116277,412879256,1555048142,5880591163,

%U 22319380999,84992915958,324634976440,1243396473153,4774504667881,18376620653851,70883537152927

%N G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^4.

%F a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * binomial(4*k,k) / (3*k+1).

%o (PARI) a(n) = sum(k=0, n\2, binomial(n, 2*k)*binomial(4*k, k)/(3*k+1));

%Y Cf. A110199, A364593.

%Y Cf. A364592, A364596.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Jul 29 2023