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Introduction to generatingfunctionology (yes, the single-word typesetting is a joke, but blame Wilf for it, not me), via Pascal's triangle again: (1+x n as a generating polynomial for the nth row, proved by induction and used to re-explain the fact that the sum of all the entries in that row is 2n and to find the sum of their squares via the xn coefficient of (1+x n (1+x n = (1+x 2n.