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G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(-2^n) )...)^-4)^-2)^-1.
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%I #3 Mar 30 2012 18:36:58

%S 1,1,-1,3,-16,145,-2347,72498,-4459887,554300965,-139235329270,

%T 70475747813447,-71685052573258824,146249172542467865074,

%U -597744865134782025119044,4890851047359454263328433041,-80078758027845307168595201926254

%N G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(-2^n) )...)^-4)^-2)^-1.

%C Limit |a(n)|/2^[(n-1)*(n-2)/2] = 1.97254925752982255...

%e G.f.: A(x) = 1 + x/B(x); B(x) = 1 + x/C(x)^2; C(x) = 1 + x/D(x)^4;

%e D(x) = 1 + x/E(x)^8; E(x) = 1 + x/F(x)^16; ...

%e where the respective sequences begin:

%e B=[1,1,-2,11,-112,2025,-67324,4305909,-545113744,...];

%e C=[1,1,-4,42,-836,30259,-2041616,265712044,-68214603840,...];

%e D=[1,1,-8,164,-6456,467850,-63614840,16702037652,...];

%e E=[1,1,-16,648,-50736,7358500,-2008876560,1059405119352,...];

%e F=[1,1,-32,2576,-402272,116732040,-63860549280,...].

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n, A=1+x/A^(2^(n-j))); polcoeff(A, n)}

%Y Cf. A120959 (variant).

%K sign

%O 0,4

%A _Paul D. Hanna_, Aug 09 2006