# Problem 427: n-sequences
A sequence of integers S = {si} is called an n-sequence if it has n
elements and each element si satisfies 1 ≤ si ≤ n. Thus there are nn
distinct n-sequences in total. For example, the sequence S = {1, 5, 5,
10, 7, 7, 7, 2, 3, 7} is a 10-sequence. For any sequence S, let L(S) be
the length of the longest contiguous subsequence of S with the same
value. For example, for the given sequence S above, L(S) = 3, because of
the three consecutive 7's. Let f(n) = ∑ L(S) for all n-sequences S. For
example, f(3) = 45, f(7) = 1403689 and f(11) = 481496895121. Find
f(7 500 000) mod 1 000 000 009.