I would make the same GUESS as MarkFL, because it makes some nice patterns: each number is 1 more than a (descending) power of 2; the differences are descending powers of 2.
But any number could be put there, and it would still be a sequence. (Series is not really the right word.)
A question like this is not really a math problem, but a psychological test: do you see the same shape in this ink blot as the author did? People familiar with certain types of math are likely to see the same thing, but that doesn't really make it more correct than any other.
As pointed out already, 17 is one of many correct answers. There are for example MANY polynomials that pass through the points (1,65),(2, 33) and (4, 9). Any one of those formulas (polynomial equations) would work to find the missing number.