There IS...or There ARE a book and a pen on the table?

You may find different answers to this question depending on whom you ask, but almost all native speakers of English would definitively agree that they would say:

"There IS a book and a pen on the table."

The argument for "There are" is that "a book and a pen" are plural.  In that case, it sounds much better to say:

A book and a pen are on the table.

BUT when using the dummy subject "There", it sounds better to say:

There is a book (and there is) a pen on the table.

The rule at work here is that it sounds strange to have a plural verb (are) right next to a singular subject (a book), and vice versa.  It sounds strange to have a singular verb (is) next to a plural subject (pens).  

Ex.  There is a book and pens on the table.

       There are a book and pens on the table.

       There are pens and a book on the table.

       There are a book and pens on the table.  

Ex. There is a girl and two boys waiting outside for us.
       There are a girl and two boys waiting outside for us.
       There are boys and a girl on the soccer team.
       There are a girl and boys on the soccer team.