_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jan 17 2011

proposed

approved

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

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

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

(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)}

Cf. A120959, A184576, A184577.

allocated for Paul D. Hanna

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

1, 1, 3, 30, 892, 76554, 19138212, 14126533902, 31053145918644, 204151364083796877, 4021430292908836847748, 237530957105884844479669995, 42082478775006270167542801189164, 22365250673182738144111737076795384386

0,3

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

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

Related functions are defined by:

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

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

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

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

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

where the coefficients in the above functions begin:

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

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

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

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

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

(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)}

Cf. A120959, A184576, A184577.

allocated

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jan 17 2011

approved

proposed

allocating

allocated

allocated for Paul D. Hanna

allocating

approved