cp's OEIS Frontend

A136752 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,...

%I A136752 #2 Mar 30 2012 18:37:09
%S A136752 1,1,2,3,6,10,19,33,61,108,198,354,645,1159,2106,3795,6874,12405,
%T A136752 22457,40560,73374,132578,239782,433362,783602,1416401,2560953,
%U A136752 4629393,8369741,15130440,27354520,49451349,89401972,161622356,292191262
%N A136752 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 A136752 The composition transpose of A136753.
%e A136752 G.f.: A(x) is the limit of composition of functions x/(1-x^{2^n}):
%e A136752 F_0(x) = x/(1-x)
%e A136752 F_1(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...
%e A136752 F_2(x) = F_2(x/(1-x^4)) = x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 +...
%e A136752 F_3(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) =
%e A136752 x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 + 33x^8 + 61x^9 + 108x^10 +...
%o A136752 (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 A136752 Cf. A136753; variants: A136750, A136751, A119470, A119471.
%K A136752 nonn
%O A136752 0,3
%A A136752 _Paul D. Hanna_, Jan 21 2008