title: Multiplying value corresponding to a label in one dataframe by all values with the same label in another dataframe
body: <p>I have the two following dataframes:</p>
  <pre><code>df.head()
  Out[256]: 
             NUTS_ID        t2m        HDD    DK_HDD
  Date                                              
  2018-01-01     AT1   3.501755  14.498245  0.005033
  2018-01-02     AT1   7.686142  10.313858  0.003580
  2018-01-03     AT1  10.249952   7.750048  0.002690
  2018-01-04     AT1  14.330340   3.669660  0.001274
  2018-01-05     AT1   2.928884  15.071116  0.005232
  
  df2.head()
  Out[257]: 
                  2016         2017            2018  
  NUTS_ID                                               
  AT1      5104.023345  4422.809561     4363.874907  
  AT2      3904.562866  3383.436322     3338.351485  
  AT3      6954.504900  6026.314672     5946.013052  
  BE1         0.000000     0.000000     2724.610387  
  BE2         0.000000     0.000000    14187.414251  
  </code></pre>
  <p>I want to multiply the value in <code>df2</code> corresponding to each index in one column by all the values in a column of <code>df</code> with the same code. As an example: In <code>df2</code>, I want to take the value corresponding to index <code>AT1</code> and column <code>2018</code> (4363.874907) and multiply it by all the values in the column <code>DK_HDD</code> with <code>NUTS_ID = AT1</code>, then the same for <code>AT2</code>, and so on.</p>
  <p>The result I expect would be a new dataframe with the structure:</p>
  <pre><code>           NUTS_ID    Product
  Date                                              
  2018-01-01     AT1    21.9633
  2018-01-02     AT1    15.6226
  2018-01-03     AT1    11.7388
  2018-01-04     AT1     5.5595
  2018-01-05     AT1    22.8317 
  </code></pre>
  <p>I tried using <code>mul</code> but I got NaN and also lost the <code>NUTS_ID</code> column. What would be the best way to do this? Thanks in advance.</p>
  <p>Just in case it's necessary:</p>
  <pre><code>df.dtypes
  Out[262]: 
  NUTS_ID     object
  t2m        float64
  HDD        float64
  DK_HDD     float64
  dtype: object
  
  df2.dtypes
  Out[263]: 
  2016    float64
  2017    float64
  2018    float64
  dtype: object
  </code></pre>