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Expansion of F(x) where F(x) = 1 + x / (1 - x * F(x^2)^2 ).
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%I #5 Mar 01 2014 02:12:16

%S 1,1,1,1,3,5,10,19,36,69,135,258,500,963,1862,3592,6940,13393,25869,

%T 49939,96437,186190,359531,694176,1340393,2588071,4997263,9648958,

%U 18630886,35973552,69460077,134117616,258962680,500020761,965470897,1864189893,3599491983,6950118531,13419713384,25911601377

%N Expansion of F(x) where F(x) = 1 + x / (1 - x * F(x^2)^2 ).

%C What does this sequence count?

%C a(n+1)/a(n) tends to 1.9308610132631268... - _Vaclav Kotesovec_, Feb 28 2014

%o (PARI)

%o N=66; R=O('x^N); x='x+R;

%o F = 1; for (k=1, N+1, F = 1 + x / (1 - x * subst(F, 'x, 'x^2)^2 ) + R; );

%o Vec(F)

%K nonn

%O 0,5

%A _Joerg Arndt_, Feb 28 2014