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%I #2 Mar 30 2012 18:37:09
%S 1,1,3,31,1327,170211,68333813,89675072255,397525147082217,
%T 6103188627225900995,331088233835064606501621,
%U 64490029272314754165301653295,45679131008965219349145151231118965
%N G.f. A(x) satisfies: 1+x = Sum_{n>=0} C(2^n,n) * x^n / A(x)^(2^n).
%F G.f. A(x) satisfies: 1+x = Sum_{n>=0} log( (1 + 2^n*x)/A(x) )^n / n!.
%e G.f. A(x) = 1 + x + 3*x^2 + 31*x^3 + 1327*x^4 + 170211*x^5 + ...
%e 1 + x = Sum_{n>=0} C(2^n,n) * x^n * A(x)^(-2^n) =
%e (1 - x - 2x^2 - 26x^3 - 1264x^4 - 167480x^5 - 67988870x^6 -...) +
%e .2x*(1 - 2x - 3x^2 - 48x^3 - 2472x^4 - 332328x^5 -...) +
%e ...6x^2*(1 - 4x - 2x^2 - 84x^3 - 4743x^4 - 654480x^5 -...) +
%e .......56x^3*(1 - 8x + 12x^2 - 152x^3 - 8810x^4 -...) +
%e ..........1820x^4*(1 - 16x + 88x^2 - 496x^3 - 15044x^4 -...) +
%e ..............201376x^5*(1 - 32x + 432x^2 - 3808x^3 -...) +
%e ..................74974368x^6*(1 - 64x + 1888x^2 +...) + ...
%o (PARI) {a(n)=local(A=[1,1]);if(n<0,0,if(n==0,1,for(i=0,n-1,A=concat(A,0); A[ #A]=Vec(sum(n=0,#A-1,log((1+2^n*x)/Ser(A))^n/n!))[ #A]);A[n+1]))}
%Y Cf. A014070 (C(2^n, n)).
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 09 2008
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