cp's OEIS Frontend

A136753 G.f.: A(x) = ...o x/(1-x^8) o x/(1-x^4) o x/(1-x^2) o x/(1-x), composition of functions x/(1 - x^{2^n}) for n=...,3,2,1,0.

%I A136753 #2 Mar 30 2012 18:37:09
%S A136753 1,1,2,4,9,21,52,134,355,955,2590,7052,19246,52638,144368,397468,
%T A136753 1099720,3060936,8577496,24210808,68843806,197176726,568585576,
%U A136753 1649739332,4812731846,14105205846,41498665884,122469937048
%N A136753 G.f.: A(x) = ...o x/(1-x^8) o x/(1-x^4) o x/(1-x^2) o x/(1-x), composition of functions x/(1 - x^{2^n}) for n=...,3,2,1,0.
%C A136753 The composition transpose of A136752.
%e A136753 G.f.: A(x) is the limit of composition of functions x/(1-x^{2^n}):
%e A136753 F_0(x) = x/(1-x)
%e A136753 F_1(x) = x/(1-x^2) o F_0(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...
%e A136753 F_2(x) = x/(1-x^4) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
%e A136753 F_3(x) = x/(1-x^8) o F_2(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
%e A136753 F_4(x) = x/(1-x^16) o x/(1-x^8) o x/(1-x^4) o x/(1-x^2) o x/(1-x) =
%e A136753 x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 21*x^6 + 52*x^7 + 134*x^8 + 355*x^9 +...
%o A136753 (PARI) {a(n)=local(A=x+x*O(x^n));if(n<=0,0,for(i=0,#binary(n+1),A=A/(1-A^(2^i)));polcoeff(A,n))}
%Y A136753 Cf. A136752; variants: A136750, A136751, A119470, A119471.
%K A136753 nonn
%O A136753 1,3
%A A136753 _Paul D. Hanna_, Jan 21 2008