About
> G.F.: (1+x)(1+2x^2)(1+x^3)(1+2x^4)(1+2x^8)(1+2x^16)(1+2x^32)(1+2x^64)
versus
G.F.: (1+x)(1+x^2)^2(1+x^3)(1+x^4)^2(1+x^8)^2(1+x^16)^2(1+x^32)^2(1+x^64)^2
The first accounts for ordered sorts, the second for un-ordered
which is more common with partitions. "Ordered" is more common
with compositions ("ordered partitions").
Regards, jj