.A sequence of numbers is called 'uber' if for any k, k-1 appears at least once before the last(rightmost) k. What is the number of uber sequences of length n? For example, 111111 is uber, 321234 is uber, but 22221 is not uber. (Hint : Try counting number of uber sequences of length 2, length 3, length 4. From this can you make an educated guess for n in general?)

. proof for \sum_{i from k to n} c(n,i) (i choose k) = c(n+1,k+1)