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.

1, 1, 2, 4, 9, 21, 52, 134, 355, 955, 2590, 7052, 19246, 52638, 144368, 397468, 1099720, 3060936, 8577496, 24210808, 68843806, 197176726, 568585576, 1649739332, 4812731846, 14105205846, 41498665884, 122469937048

Offset

1,3

Comments

The composition transpose of A136752.

Links

Table of n, a(n) for n=1..28.

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) = x/(1-x^2) o F_0(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...
F_2(x) = x/(1-x^4) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
F_3(x) = x/(1-x^8) o F_2(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
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) =
x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 21*x^6 + 52*x^7 + 134*x^8 + 355*x^9 +...

Prog

(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))}

Crossrefs

Cf. A136752; variants: A136750, A136751, A119470, A119471.

Sequence in context: A000636 A204352 A195980 * A289666 A084261 A063026

Adjacent sequences: A136750 A136751 A136752 * A136754 A136755 A136756

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2008

Status

approved