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G.f. satisfies A(x) = 1 + x * A(x)^2 * (1 + A(x))^2.
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%I #18 Apr 02 2024 08:53:50

%S 1,4,48,784,14784,302976,6555648,147380480,3408817152,80592320512,

%T 1938923790336,47314993324032,1168315059240960,29136848453632000,

%U 732857340425011200,18569095605771632640,473534596510970019840,12144227894941523116032

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

%H Seiichi Manyama, <a href="/A371658/b371658.txt">Table of n, a(n) for n = 0..694</a>

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

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

%Y Cf. A219534, A219537, A371657.

%Y Cf. A025225, A371655, A371661.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 01 2024