I believe this is what you want:
table.groupby('YEARMONTH').CLIENTCODE.nunique()
Example:
In [2]: table
Out[2]:
CLIENTCODE YEARMONTH
0 1 201301
1 1 201301
2 2 201301
3 1 201302
4 2 201302
5 2 201302
6 3 201302
In [3]: table.groupby('YEARMONTH').CLIENTCODE.nunique()
Out[3]:
YEARMONTH
201301 2
201302 3
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