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%I #11 Sep 23 2016 14:20:56
%S 1,1,-2,13,-145,2328,-49784,1358965,-46076544,1902202515,-94104681660,
%T 5503867176832,-376096374571125,29714871818774044,
%U -2689473418781240320,276562260699626541509,-32073434441440654231749,4167256779254698145624064,-603002974281204853457239860
%N Bisection (odd-indexed terms) of A107700.
%H P. Majer, <a href="http://mathoverflow.net/questions/49724/">The functional equation f(f(x))=x+f(x)^2</a>
%F G.f.: A(x) = (G(x) - G(-x))/2, where G(x) is the g.f. of A107700 and satisfies: G(G(x)) = x + 2*G(x)^2.
%t a[n_] := Module[{A, B, F}, A = Series[x+x^2+x^(2*n), {x, 0, 2*n}]; If[n<1, 0, For[i=0, i <= 2*n, i++, F = x+2*A^2; B = InverseSeries[A]; A = (A+(B /. x -> F))/2]; SeriesCoefficient[A, {x, 0, 2*n-1}]]]; Table[a[n], {n, 1, 19}] (* _Jean-François Alcover_, Feb 04 2014, after PARI *)
%o (PARI) {a(n)=local(A,B,F);A=x+x^2+x*O(x^(2*n));if(n<1,0, for(i=0,2*n,F=x+2*A^2;B=serreverse(A);A=(A+subst(B,x,F))/2); polcoeff(A,2*n-1,x))}
%Y Cf. A107700, A107701.
%K sign
%O 1,3
%A _Paul D. Hanna_, May 21 2005