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12 Generating Functions - MIT OpenCourseWare

12 Generating Functions - MIT OpenCourseWare

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IMPLIES h1;2;3;4;:::i ! 1.1 x/2: (12.1) We found a generating function for the sequence h1;2;3;4;:::iof positive inte-gers! In general, differentiating a generating function has two effects on the corre-sponding sequence: each term is multiplied by its index and the entire sequence is shifted left one place. Rule 12.2.4 (Derivative Rule). If

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