A136750 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.

1, 1, 2, 4, 8, 17, 35, 74, 155, 329, 692, 1464, 3098, 6553, 13873, 29361, 62165, 131638, 278787, 590357, 1250337, 2648108, 5608735, 11879607, 25161906, 53295451, 112886028, 239108343, 506466366, 1072776347, 2272316123, 4813150684

Offset: 0

Author

Paul D. Hanna, Jan 21 2008

Keywords

• nonn

Comments

The composition transpose of A136751.

Examples

			G.f.: A(x) is the limit of composition of functions x/(1-x^n):
F_1(x) = x/(1-x)
F_2(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...
F_3(x) = F_2(x/(1-x^3)) = x + x^2 + 2x^3 + 4x^4 + 7x^5 + 14x^6 + 26x^7 +...
F_4(x) = F_3(x/(1-x^4)) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 + 32x^7 +...
F_5(x) = F_4(x/(1-x^5)) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 17x^6 + 34x^7 +...
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) =
x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 35*x^7 + 73*x^8 + 152*x^9 +...
		

Crossrefs

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

Programs

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))}
for(n=1,30,print1(a(n),", "))