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%I #8 Mar 30 2012 18:39:10
%S 1,1,2,8,168,82432,26984838984,4014812889317061030144,
%T 126245518036918986681661715832901630563334656,
%U 174032897098486613071748425543428287864783701646257306342693313602518201638203850484486144
%N Let P(n,x) be defined as follows : P(1,x)=x P(n,x)=P(n-1,x)^2+1, sequence gives maximum value of coefficients of P(n,x).
%e P(4,x)= x^8 + 4*x^6 + 8*x^4 + 8*x^2 + 5 hence a(4)=8
%t f[n_] := Block[{k = n - 2}, Max@ CoefficientList[ Expand@ Nest[(1 + #)^2 &, x, k], x]]; f[1] = 1; Array[f, 10]
%o (PARI) b(n)=if(n<2,x,b(n-1)^2+1); a(n)=vecmax(vector(2^n/2/2,i,polcoeff(b(n),2*i,x)))
%K nonn
%O 1,3
%A _Benoit Cloitre_, Oct 19 2002
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