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

%I #4 Mar 01 2014 02:09:27

%S 1,1,1,2,3,6,13,29,65,151,359,864,2100,5160,12796,31952,80272,202821,

%T 515057,1313716,3364049,8645559,22291985,57649712,149496257,388647248,

%U 1012717568,2644555020,6919609962,18139104129,47632278280,125282210973,330016728365,870564606345,2299577632573,6081963356452

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

%C What does this sequence count?

%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 * F * subst(F, 'x, -'x^2) ) + R; );

%o Vec(F)

%Y Cf. A238427: F(x) = 1 + x / (1 - x * F(x) * F(+x^2) ).

%K nonn

%O 0,4

%A _Joerg Arndt_, Feb 28 2014