seq A100661

[Ralf Stephan]

You wrote 
> http://www.research.att.com/~njas/sequences/A100661
> 
> The following _seems_ to be true:
> 
> OGF =  \frac{2\,(1-x)\,\prod_{n=1}^{\infty}{\left(1+x^{2^n-1}\right)} - 1}{(1-x)^2}

Intuitively, this is all true as, from experience, if you start with
such OGFs (sums or products where x is to the 2 to the index) you
will get sequences that have connecions to the binary representation.
The OEIS is full of such sequences.


ralf