Thirteen friends decide to go to the movies. In the theater there are rows of 13 seats. For some stupid reason they decide that the first person to enter the row may sit wherever he chooses. The second person must sit on either side of him with no empty seat between. The third person may sit on either side of the first two as long as no empty seat is between them. This procedure continues until all are seated.
How many different seating arrangements are possible?