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%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
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