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A137984 G.f.: A(x) = 1/(1 - 2*x*[A_1(x)]^(1/2)); A_1(x) = 1/(1 - 4*x*[A_2(x)]^(1/4)); ...; where A_{n-1}(x) = 1/(1 - 2^n*x*[A_{n}(x)]^(1/2^n)) for n>=1 with A_0(x)=A(x). 1

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

%S 1,2,8,44,304,2572,26720,347832,5857280,132320524,4142751104,

%T 183830444712,11695392882688,1070962802526776,141154845280097280,

%U 26736918028187247344,7263732704774358982656,2824813896305950802751372

%N G.f.: A(x) = 1/(1 - 2*x*[A_1(x)]^(1/2)); A_1(x) = 1/(1 - 4*x*[A_2(x)]^(1/4)); ...; where A_{n-1}(x) = 1/(1 - 2^n*x*[A_{n}(x)]^(1/2^n)) for n>=1 with A_0(x)=A(x).

%e G.f.: A(x) = 1 + 2*x + 8*x^2 + 44*x^3 + 304*x^4 + 2572*x^5 +...;

%e A_1(x) = 1 + 2*x + 10*x^2 + 72*x^3 + 670*x^4 + 7824*x^5 +...;

%e A_2(x) = 1 + 2*x + 14*x^2 + 144*x^3 + 1934*x^4 + 32896*x^5 +...;

%e A_3(x) = 1 + 2*x + 22*x^2 + 352*x^3 + 7262*x^4 + 188352*x^5 +...;

%e A_4(x) = 1 + 2*x + 38*x^2 + 1024*x^3 + 34494*x^4 + 1425856*x^5 +...;

%e A_5(x) = 1 + 2*x + 70*x^2 + 3392*x^3 + 198270*x^4 + 13714368*x^5 +...; ...

%e where

%e A(x) = 1/(1 - 2*x*[A_1(x)]^(1/2));

%e A_1(x) = 1/(1 - 4*x*[A_2(x)]^(1/4));

%e A_2(x) = 1/(1 - 8*x*[A_3(x)]^(1/8));

%e A_3(x) = 1/(1 - 16*x*[A_4(x)]^(1/16));

%e A_4(x) = 1/(1 - 32*x*[A_5(x)]^(1/32)); ...

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 25 2008

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Last modified April 12 19:05 EDT 2024. Contains 371636 sequences. (Running on oeis4.)