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,...

1, 1, 2, 3, 6, 10, 19, 33, 61, 108, 198, 354, 645, 1159, 2106, 3795, 6874, 12405, 22457, 40560, 73374, 132578, 239782, 433362, 783602, 1416401, 2560953, 4629393, 8369741, 15130440, 27354520, 49451349, 89401972, 161622356, 292191262

Offset

0,3

Comments

The composition transpose of A136753.

Links

Table of n, a(n) for n=0..34.

Example

G.f.: A(x) is the limit of composition of functions x/(1-x^{2^n}):
F_0(x) = x/(1-x)
F_1(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...
F_2(x) = F_2(x/(1-x^4)) = x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 +...
F_3(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) =
x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 + 33x^8 + 61x^9 + 108x^10 +...

Prog

(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))}

Crossrefs

Cf. A136753; variants: A136750, A136751, A119470, A119471.

Sequence in context: A079959 A282583 A028495 * A093126 A003237 A191519

Adjacent sequences: A136749 A136750 A136751 * A136753 A136754 A136755

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2008

Status

approved