Concrete mathematics : a foundation for computer science

65 Prove that
Ck(k+l)! = n.
66 Evaluate “Harry’s double sum,’
given an integer n 3 0.
as a function of m. (The sum is over both j and k.)
67 Find a closed form for
g ($)) (‘“nik) , integer n 3 0.
68 Find a closed form for
69 Find a closed form for
min
kl ,...,k,>O
k,+...+k,=n
as a function of m and n.
70 Find a closed form for
71 Let
integer n > 0.
c (3 ri) (+)” , integer n 3 0.
5 EXERCISES 237
where m and n are nonnegative integers, and let A(z) = tk,o okzk be
the generating function for the sequence (CQ, al, al,. . . ).
a Express the generating function S(z) = &c S,Z” in terms of A(z).
b Use this technique to solve Problem 7 in Section 5.2.