code: def test_series_groupby_value_counts_empty(columns):
      # GH39172
      df = DataFrame(columns=columns)
      dfg = df.groupby(columns[:-1])
  
      result = dfg[columns[-1]].value_counts()
      expected = Series([], dtype=result.dtype, name="count")
      expected.index = MultiIndex.from_arrays(
          [[]] * len(columns), names=columns
      )
  
      tm.assert_series_equal(result, expected)
  
imports: import numpy
  import pytest
  import pandas.util._test_decorators
  from pandas import Categorical, CategoricalIndex, DataFrame, Grouper, Index, MultiIndex, Series, date_range, to_datetime
  import pandas._testing
  from pandas.util.version import Version
label_desc: Use image node_id 5 for calling a global function with example usage: test_series_groupby_value_counts_empty(columns) without return types