Sequence Defined In Terms Of EVERY Term In It

[N. J. A. Sloane]

Leroy,  The sequences in my paper on "Canonical sequences"
with Mira Bernstein can be regarded as examples of that type,
I think.  See for example A007560.  Such sequences usually
have keyword "eigen".

Your example

{a[k]} is such that:

sum{k=0 to oo} a[k] *x^k =

product{k=0 to oo} (1 +a[k]*x),

is of this form - but we usually found it necessary to 
shift the a[] sequence by one click on say the right-hand
side of the equation in order to get an interesting sequence.

You can download the paper from
(<a href="http://www.research.att.com/~njas/doc/eigen.txt">Abstract</a>, <a href="http://www.research.att.com/~njas/doc/eigen.pdf">pdf</a>, <a href="http://www.research.att.com/~njas/doc/eigen.ps">ps</a>)

NJAS