A184576 G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(4^n) )...)^64)^16)^4.

1, 1, 4, 70, 4772, 1256737, 1300189840, 5343387957552, 87635577037531120, 5745017883201162928720, 1506152833843572741772875256, 1579354544764797425414872390884936, 6624338541974058042578557252396267711144

Offset

0,3

Comments

Limit a(n)/4^[n(n-1)/2] = 1.2167020033386380312738338894882216...

Links

Table of n, a(n) for n=0..12.

Example

 G.f.: A(x) = 1 + x + 4*x^2 + 70*x^3 + 4772*x^4 + 1256737*x^5 +...
Related functions are defined by:
A(x) = 1 + x*B(x)^4;
B(x) = 1 + x*C(x)^16;
C(x) = 1 + x*D(x)^64;
D(x) = 1 + x*E(x)^256;
E(x) = 1 + x*F(x)^1024; ...
where the coefficients in the above functions begin:
B=[1,1,16,1144,310320,324057372,1334856912400,21904872061736520,...];
C=[1,1,64,18400,19940032,83109401072,1367783819781952,...];
D=[1,1,256,294784,1277438720,21285675278272,1400838812478999808,...];
E=[1,1,1024,4718080,81776520192,5449752029298432,1434517374576707974144,...];
F=[1,1,4096,75495424,5234024427520,1395176151497833472,...].

Prog

 (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)}

Crossrefs

Cf. A120959, A184575, A184577.

Sequence in context: A301586 A367434 A136465 * A367523 A162135 A047939

Adjacent sequences: A184573 A184574 A184575 * A184577 A184578 A184579

Keyword

nonn

Author

Paul D. Hanna, Jan 17 2011

Status

approved