Your data has some duplicates in columns name, so melt will fail. However, you could change columns name and then apply melt
In [166]: df
Out[166]:
A B C D E F G H G H I J K
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Duplicates in column name 'G' and 'H'. Just change those to 'GG', 'HH'. Finally, apply melt
In [167]: df.columns = ('A','B','C','D','E','F','G','H','GG','HH','I','J','K')
In [168]: df
Out[168]:
A B C D E F G H GG HH I J K
0 1 2 3 4 5 6 7 8 9 10 11 12 13
In [169]: df.melt(id_vars=df.columns.tolist()[0:7], value_name='H').drop('variable', 1)
Out[169]:
A B C D E F G H
0 1 2 3 4 5 6 7 8
1 1 2 3 4 5 6 7 9
2 1 2 3 4 5 6 7 10
3 1 2 3 4 5 6 7 11
4 1 2 3 4 5 6 7 12
5 1 2 3 4 5 6 7 13