Incomplete words
Problem 657
In the context of formal languages, any finite sequence of letters of a given alphabet is called a word over . We call a word incomplete if it does not contain every letter of .
For example, using the alphabet , '', '' and '' (the empty word) are incomplete words over , while '' is a complete word over .
Given an alphabet of letters, we define to be the number of incomplete words over with a length not exceeding .
For example, , and .
For example, , and .
Find . Give your answer modulo .