Unformatted text preview: e x1) 2 e x . We want the coe ﬃ cient of x r in this. We have ( e x1) 2 e x = ( e 2 x2 e x + 1) e x = e 3 x2 e 2 x + e x . Using the Taylor series for e x this is equal to ∞ X r = 3 r x r r !∞ X r = 2 r + 1 x r r ! + ∞ X r = x r r ! So the coe ﬃ cient of x r r ! is 3 r2 r + 1 + 1. 1...
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 Spring '11
 Raghaven
 XR, Generating function, ordinary generating function, Dilip Raghavan

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