Primary Key with serial

Hi,


   I have the following table    create table product(cod serial, user_cod bigint, constraint product_fk Foreign Key(user_cod) references user(cod), constraint product_pk Primary Key(cod, user_cod));

What i want to happend is that:
user_cod            cod
1                         1
1                         2
1                         3
2                         1
3                         1
3                         2

Can serial do that? If not, what can  i do to make this happen?

Thanks a lot