Is there any interest in improving SymPy's handling of sequences as a GSoC
project? As a mathematics student, I often find myself checking identities
involving well-known, recursive sequences and their generating functions. 
When
I use SymPy to do this I always end up cobbling together something that 
works,
but is never quite satisfying.

I think that a rough set of goals would be this:

- Improve recursive sequence handling.

    I took a stab at implementing a recursive sequence class earlier this 
year,
    but after using it for a while I think it could be better.

- Improve sequence usage throughout SymPy.

    For instance, `rsolve` returns an expression, not a sequence.

- Implement well-known classes of sequences (C-finite, etc.).

    Some of this exists scattered throughout SymPy. It should be organized 
into
    a cohesive module.

- Improve sequence documentation.

This isn't quite in line with the listed mathematics projects from last 
year,
but I think it could be useful.

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