Experts and BHG readers answer.
Most commercial pumpkins have both male and female flowers, but a few varieties have only female flowers. When such types are sold, seed companies always include seeds of a normal type that sets both male and female flowers, so the male flowers can provide pollen for the all-female plants. Because you had only one vine, if it was one that forms only female flowers and there wasn't any other pumpkin (or zucchini-type squash) around to pollinate it, it would produce blooms but would fail to set any pumpkins. It's possible that the plant had male and female flowers but none was pollinated. Did you notice any insects, such as bees, around the flowers? If they were absent, that may be the reason. You can distinguish male and female flowers by looking under the flower. Male flowers have a slender stalk attaching them to the vine. Female flowers have a swollen base that looks like a miniature pumpkin. If both are present on your vine, you can compensate for lack of insect pollinators by hand-pollinating the female blossoms. Take an artist's brush to gather pollen from the male blossom early in the morning. Transfer the pollen to a freshly opened female blossom. Within a few days you should see the swollen base beginning to enlarge into a pumpkin.