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%I #4 Mar 30 2012 18:37:25
%S 1,1,4,70,4772,1256737,1300189840,5343387957552,87635577037531120,
%T 5745017883201162928720,1506152833843572741772875256,
%U 1579354544764797425414872390884936,6624338541974058042578557252396267711144
%N G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(4^n) )...)^64)^16)^4.
%C Limit a(n)/4^[n(n-1)/2] = 1.2167020033386380312738338894882216...
%e G.f.: A(x) = 1 + x + 4*x^2 + 70*x^3 + 4772*x^4 + 1256737*x^5 +...
%e Related functions are defined by:
%e A(x) = 1 + x*B(x)^4;
%e B(x) = 1 + x*C(x)^16;
%e C(x) = 1 + x*D(x)^64;
%e D(x) = 1 + x*E(x)^256;
%e E(x) = 1 + x*F(x)^1024; ...
%e where the coefficients in the above functions begin:
%e B=[1,1,16,1144,310320,324057372,1334856912400,21904872061736520,...];
%e C=[1,1,64,18400,19940032,83109401072,1367783819781952,...];
%e D=[1,1,256,294784,1277438720,21285675278272,1400838812478999808,...];
%e E=[1,1,1024,4718080,81776520192,5449752029298432,1434517374576707974144,...];
%e F=[1,1,4096,75495424,5234024427520,1395176151497833472,...].
%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(4^(n-j))); polcoeff(A, n)}
%Y Cf. A120959, A184575, A184577.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 17 2011
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