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%I #8 Oct 23 2015 19:55:42
%S 1,1,2,7,26,124,596,3365,18954,120242,760140,5281436,36617556,
%T 274624708,2059397032,16520347463,132773992954,1132184343204,
%U 9689336590700,87424470404886,792807348829740,7541745922428356,72187384283011000
%N G.f. satisfies: A(x - x*B(x)) = x where B(x) = (A(x) - A(-x))/2, the odd bisection of A(x).
%C a(n) == 1 (mod 2) iff n = 2^k for k>=0.
%H Paul D. Hanna, <a href="/A141203/b141203.txt">Table of n, a(n) for n = 1..300</a>
%e G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 26*x^5 + 124*x^6 + 596*x^7 +...
%e The series reversion of A(x) = x - x*[A(x) - A(-x)]/2, thus:
%e A(x - x^2 - 2*x^4 - 26*x^6 - 596*x^8 - 18954*x^10 -...) = x.
%o (PARI) {a(n)=local(A=x+x^2);for(i=0,n,A=serreverse(x-x/2*(A-subst(A,x,-x+x*O(x^n))))) ;polcoeff(A,n)}
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jun 13 2008
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