[seqfan] Re: polynomial-to-product transform

[Henry Gould]

Zak, are your familiar with the paper "Power Product Expansions", by H. 
Gingold, H. W. Gould and M. E. Mays, which appeared in Utilitas 
Mathematics, 34(1988),143-161?
If not, then your result below sheds some light om what we called Power 
Product Expansions (PPE for short). We studied the general expansion

prod((1+f(i)x^i), i=1,2,...) = sum(1+g(k)x^k, k=1,2,...)

and summarized the literature. Gingold has used the PPE idea for various 
purposes since 1988. I think you should look at our paper.
Henry Gould
- - - - - - -
zak seidov wrote:
> Suprisingly,
>
> prod((1+a(i)x^i), i=1,2,...) => sum(1+prime(n)x^k, k=1,2,...)
>
> gives  a(i) = 2, 3, -1, 9, -4, -16, 89,... 
>
> not in OEIS?! or i'm terribly missing smth, zak
>
>
>       
>
>
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