DOC/CI: include api docs on travis
Continuation of #11069 (It seems I cannot reopen that PR because I already force pushed the branch ..)

Closes #3800

TODO:
- [x] remove printing of doc build log file in after_script

Reason for reopening this, is that I noticed that sphinx 1.3 seemed to be improved in performance. And indeed, now the doc build on travis takes less than 20 minutes, while before it hit the maximum travis run time of 50 min.
 @jreback Can you have a look at this? Note that there is still one temp commit that should be removed, so the full diff is not fully correct (and I also need to rebase)

This is related to https://github.com/pydata/pandas/issues/12003 (@shoyer), but I think this is still relevant. Maybe not necessarily for building the dev docs (if we start using RTD for this), but you can always check the doc build log for PRs this way.
 ```
./make.py
sh: 1: jupyter: not found
Running Sphinx v1.3.3
```

do you need to add jupyter to the install?
 Rebased, removed the temporary commit, and added `nbconvert` as a dependency
 FYI, I saw [nbsphinx](http://nbsphinx.readthedocs.org/en/0.2.3/) the other day. I ran it on our style notebook and it seemed to work pretty well. There were a few CSS things that don't get picked up properly, but we can probably move to that soon.
 @jorisvandenbossche this looks good.

only thing (and can do later), is maybe move this build up so its the first one after main builds (before slow ones).
 merge when ready (try out `merge-pr.py`)
 @jorisvandenbossche 

build on master: https://travis-ci.org/pydata/pandas/jobs/104512895

failed apparently
 Thanks for noticing. Probably due to the adding of nbconvert to requirements before I merged (what will maybe have given an incompatible nbconvert and ipython version, will need to investigate that further). 
I actually already failed in the PR, but because it's one of the allowed failures, I didn't notice ...

https://github.com/pydata/pandas/pull/12138
