Unformatted text preview: x and of x 2 in the power series for 1 x1 1 (2 x +1) 3 (c) Find a formula in terms of derivatives for the number of solutions to x 1 + x 2 + x 3 + x 4 = 20 with x 2 even and x 3 divisible by 5 9. The generating functions we have been studying are called ordinary generating functions. Another class is called Exponential Generating Functions and are deﬁned as follows: The Exponenetial Generating Function for the sequence { a n } is ∞ X n =0 a n n ! x n Note the division by n !. Thus, the exponenetial generating function for 1 , 1 ,... is ∑ x n n ! = e x . Use this fact to ﬁnd a closed form for the exponenetial generating function for each of the following sequences: (a) a n = 3 n (b) a n = (1) n (c) a n = n + 1 (d) a n = 1 n +1 (Hint: reindex)...
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This note was uploaded on 09/10/2009 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.
 Summer '08
 STRAIN
 Math

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