A120959 - OEIS

%I #5 Dec 24 2013 15:43:11

%S 1,1,2,9,84,1540,54522,3734454,498851832,131025111932,68094916593416,

%T 70324929555472825,144712913119662777792,594305955799647611394896,

%U 4875569433937264188593935824,79943787791004406866072303453528

%N G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^(2^n) )...)^8)^4)^2.

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

%e G.f.: A(x) = 1 + x*B(x)^2; B(x) = 1 + x*C(x)^4; C(x) = 1 + x*D(x)^8;

%e D(x) = 1 + x*E(x)^16; E(x) = 1 + x*F(x)^32; ...

%e where the respective sequences begin:

%e B=[1,1,4,38,724,26385,1837224,247455640,65256486712,...];

%e C=[1,1,8,156,6008,436870,60346328,16118073852,8445009616488,...];

%e D=[1,1,16,632,48944,7110684,1956587408,1040720206536,...];

%e E=[1,1,32,2544,395104,114749560,63023951008,66902165283280,...];

%e F=[1,1,64,10208,3175104,1843872240,2023417888576,...].

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

%Y Cf. A234296, A095793.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 28 2006