login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 3

%I

%S 1,1,2,4,9,21,52,134,355,955,2590,7052,19246,52638,144368,397468,

%T 1099720,3060936,8577496,24210808,68843806,197176726,568585576,

%U 1649739332,4812731846,14105205846,41498665884,122469937048

%N 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 The composition transpose of A136752.

%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) = x/(1-x^2) o F_0(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...

%e F_2(x) = x/(1-x^4) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...

%e F_3(x) = x/(1-x^8) o F_2(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...

%e 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 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 (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 Cf. A136752; variants: A136750, A136751, A119470, A119471.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jan 21 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 06:45 EDT 2022. Contains 353961 sequences. (Running on oeis4.)