Since the numbers are strictly ascending, precluding duplicates and assuring exactly one representation for any set of digits present, we need only concern ourselves with combinations rather than permutations.

Again since they are ascending, the prohibition on leading zeros is a prohibition on zeros altogether.

Any of the 15 other digits, 1 through F, can either appear or not appear in the integer N, so initially we come up with 2^15. But this includes a no-digit "number" as well as 15 1-digit numbers, so the final answer is 2^15 - 16 = 32,752.