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G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(4n))...)^12)^8)^4.
6

%I #2 Mar 30 2012 18:37:09

%S 1,1,4,38,596,13137,373544,13008184,535947320,25492727304,

%T 1374588760980,82844371459764,5518323917106220,402556752045926108,

%U 31916585459440839392,2732642735337686840152,251267557458318511262096

%N G.f.: A(x) = 1 + x*(1 + x*(1 + x*(...(1 + x*(...)^(4n))...)^12)^8)^4.

%e G.f.: A(x)=1+x*B(x)^4, B(x)=1+x*C(x)^8, C(x)=1+x*D(x)^12, D(x)=1+x*E(x)^16,...

%e where A(x),B(x),C(x),... are the g.f. of the sequences given below.

%e A=[1,1,4,38,596,13137,373544,13008184,535947320,25492727304,...];

%e B=[1,1,8,124,2792,81462,2902528,121830916,5880235184,...];

%e C=[1,1,12,258,7612,278991,12084552,600710380,33615167976,...];

%e D=[1,1,16,440,16080,711740,36459968,2105685752,134824193120,...];

%e E=[1,1,20,670,29220,1517725,89938984,5933795760,429195194520,...];

%e F=[1,1,24,948,48056,2866962,193128768,14351122716,1159330814736,...]; ...

%o (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)}

%Y Cf. A095793, A138211, A138212, A138213, A138215, A138216.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 06 2008