%I #6 Mar 30 2012 18:37:25

%S 1,1,3,30,892,76554,19138212,14126533902,31053145918644,

%T 204151364083796877,4021430292908836847748,

%U 237530957105884844479669995,42082478775006270167542801189164,22365250673182738144111737076795384386

%N G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(3^n) )...)^27)^9)^3.

%C Limit a(n)/3^[n(n-1)/2] = 1.361839192264541770366149558100...

%e G.f.: A(x) = 1 + x + 3*x^2 + 30*x^3 + 892*x^4 + 76554*x^5 +...

%e Related functions are defined by:

%e A(x) = 1 + x*B(x)^3;

%e B(x) = 1 + x*C(x)^9;

%e C(x) = 1 + x*D(x)^27;

%e D(x) = 1 + x*E(x)^81;

%e E(x) = 1 + x*F(x)^243; ...

%e where the coefficients in the above functions begin:

%e B=[1,1,9,279,24870,6324282,4695640434,10341522771762,...];

%e C=[1,1,27,2538,678708,515666952,1144737153180,7549554318496218,...];

%e D=[1,1,81,22923,18390510,41861447352,278471836036890,...];

%e E=[1,1,243,206550,497133612,3393278306694,67693048457727060,...];

%e F=[1,1,729,1859679,13427919990,274923122390262,16451387497191947778,...].

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(j=0, n-1, A=1+x*A^(3^(n-j))); polcoeff(A, n)}

%Y Cf. A120959, A184576, A184577.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 17 2011