That actually depends on the project.
Programmers are always the highest in demand, There's usually anywhere around 4-10 programmers per designer and maybe 1-3 artists.
I've worked on projects where programmers outnumbered the artists, on projects where the artists were roughly equal in number to programmers, and I've been on projects where the art folks outnumbered programmers by about 4:1. And as typical, design and production are much less: each designer can often support ten or more other developers, producers often twenty or thirty.
One big reason for the discrepancy is the stage of the project. If the code base is immature and the engine is being heavily modified then there will be a larger ratio of programmers. When technology is stable, tools are mature, and everything is data driven, the need for programmers is small relative to the need for data content.
Another big reason is that different games have different needs. A hobby game may be all about a specific mechanic and rely on minimal art. An new engine for a moderate sized game will need a lot of programming to get all the parts in place. A blockbuster AAA title usually builds off of existing tools but needs an enormous pile of content. A long-running MMO can get along with nothing but content for quite some time.
Every project is different.