"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:
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 pens and a book on the table.
Ex. There is a girl and two boys waiting outside for us.
There are boys and a girl on the soccer team.