Generating functions are a general mathematical tool developed by de Moivre, Stirling, and Euler in the 18th century, and are used often in combinatorics. As usual, we start by taking a concrete example: In how many ways can you make change for a dollar? We’ll assume that we’re dealing with only five types of coins—pennies, nickels, dimes, quarters, and half dollars.
KeywordsProduct Rule Recursion Formula Separation Point Binary Representation Geometric Series
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