What you are looking for is the melt function
pd.melt(df,id_vars=['A'])
A variable value
0 1 B 2
1 5 B 6
2 9 B 10
3 13 B 14
4 1 C 3
5 5 C 7
6 9 C 11
7 13 C 15
8 1 D 4
9 5 D 8
10 9 D 12
11 13 D 16
A final sorting according to A is then necessary
pd.melt(df,id_vars=['A']).sort('A')
A variable value
0 1 B 2
4 1 C 3
8 1 D 4
1 5 B 6
5 5 C 7
9 5 D 8
2 9 B 10
6 9 C 11
10 9 D 12
3 13 B 14
7 13 C 15
11 13 D 16
Note: pd.DataFrame.sort has been deprecated in favour of pd.DataFrame.sort_values.
