jmc

There are 7 ways to choose the person who is left standing. To seat the 6 remaining people, there are 6 seats from which the first person can choose, 5 seats left for the second, and so on down to 1 seat for the last person. This suggests that there are $6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1=6!$ ways to seat the six people. However, each seating can be rotated six ways, so each seating is counted six times in this count. Therefore, for each group of 6 people, there are $6!/6=5!$ ways to seat them around the table. There are 7 different possible groups of 6 to seat (one for each person left standing), giving a total of $7\cdot 5!=\boxed{840}$ ways to seat the seven people.