The problem has been solved by Dinkypuzzled, but if the puzzle was re-worded so that more than 1 number didn't belong in the series, then the following works too:
The numbers 3, 7, 8 and 15 can be removed so the series now reads:
2, 6, 14, 30 ....
the next number is determined by multiplying the previous number by 2 and then adding 2
(2 x 2) + 2 = 6
(6 x 2) + 2 = 14
(14 x 2) + 2 = 30 .....
.....