Coupons#1572
There are different types of coupons, numbered from to , and an infinite number of closed boxes. Each box contains exactly one coupon of a certain type. From each box, you can obtain a coupon of any type with equal probability. What is the expected number of boxes you need to open to obtain at least one coupon of each type?
Each line contains a positive integer , 1 \leq n \leq 33, which is the number of coupon types.
For each value of , output the expected number of boxes to open in order to collect all types of coupons. If the answer is an integer, output the integer. If the answer is not an integer, output the integer part, a space, and the fractional part as an irreducible fraction, as shown in the example. There should be no trailing spaces at the end of the lines.
Example 1