CI: Test against Python 3.7

[TomAugspurger]

• closes TST/COMPAT: test Python 3.7 #20552
• tests added / passed
• passes git diff upstream/master -u -- "*.py" | flake8 --diff
• whatsnew entry

[TomAugspurger]

@mingwandroid do you know if c3i_test will keep these 3.7 packages around until they're in the defaults?

[mingwandroid]

I will aim to keep as much there as possible.

[jreback]

can u update install.rst and setup.py where needed

[codecov]

Codecov Report

Merging #21604 into master will not change coverage.
The diff coverage is 100%.

@@           Coverage Diff           @@
##           master   #21604   +/-   ##
=======================================
  Coverage    91.9%    91.9%           
=======================================
  Files         153      153           
  Lines       49548    49548           
=======================================
  Hits        45538    45538           
  Misses       4010     4010

Flag	Coverage Δ
#multiple	90.3% <100%> (ø)	⬆️
#single	41.78% <100%> (ø)	⬆️

Impacted Files	Coverage Δ
pandas/compat/__init__.py	58.6% <100%> (+0.17%)	⬆️
pandas/core/dtypes/common.py	94.63% <0%> (-0.02%)	⬇️

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[TomAugspurger]

Merging this, to ensure things don't slip in before the release.

[alimcmaster1]

Hey, @TomAugspurger
I see two separate PR failing CI testing running Python3.7 due to the same error:
https://travis-ci.org/pandas-dev/pandas/jobs/396604150
https://travis-ci.org/pandas-dev/pandas/jobs/396594344

Is this expected?

Thanks,

Alistair