Let Hk(n) be the number of vectors x1,...,xk for which each xi is a positive integer satis...

Let Hk(n) be the number of vectors x1,...,xk for which each xi is a positive integer satisfying 1 ≤ xi ≤ n and x1 ≤ x2 ≤ ... ≤ xk.

(a) Without any computations, argue that

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(b) Use the preceding recursion to compute H3(5).