A136750 - OEIS

%I #4 Nov 18 2016 07:05:05

%S 1,1,2,4,8,17,35,74,155,329,692,1464,3098,6553,13873,29361,62165,

%T 131638,278787,590357,1250337,2648108,5608735,11879607,25161906,

%U 53295451,112886028,239108343,506466366,1072776347,2272316123,4813150684

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

%C The composition transpose of A136751.

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

%e F_1(x) = x/(1-x)

%e F_2(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...

%e F_3(x) = F_2(x/(1-x^3)) = x + x^2 + 2x^3 + 4x^4 + 7x^5 + 14x^6 + 26x^7 +...

%e F_4(x) = F_3(x/(1-x^4)) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 + 32x^7 +...

%e F_5(x) = F_4(x/(1-x^5)) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 17x^6 + 34x^7 +...

%e F_6(x) = x/(1-x) o x/(1-x^2) o x/(1-x^3) o x/(1-x^4) o x/(1-x^5) o x/(1-x^6) =

%e x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 35*x^7 + 73*x^8 + 152*x^9 +...

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

%o for(n=1,30,print1(a(n),", "))

%Y Cf. A136751; variants: A136752, A136753, A119470, A119471.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 21 2008