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G.f.: A(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) o..., composition of functions x/(1 - x^{2^n}) for n=0,1,2,3,...
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%I #2 Mar 30 2012 18:37:09

%S 1,1,2,3,6,10,19,33,61,108,198,354,645,1159,2106,3795,6874,12405,

%T 22457,40560,73374,132578,239782,433362,783602,1416401,2560953,

%U 4629393,8369741,15130440,27354520,49451349,89401972,161622356,292191262

%N G.f.: A(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) o..., composition of functions x/(1 - x^{2^n}) for n=0,1,2,3,...

%C The composition transpose of A136753.

%e G.f.: A(x) is the limit of composition of functions x/(1-x^{2^n}):

%e F_0(x) = x/(1-x)

%e F_1(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...

%e F_2(x) = F_2(x/(1-x^4)) = x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 +...

%e F_3(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) =

%e x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 + 33x^8 + 61x^9 + 108x^10 +...

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

%Y Cf. A136753; variants: A136750, A136751, A119470, A119471.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 21 2008