The Binomial transform is a mathematical operation that transforms a sequence of numbers into another sequence through a series of binomial coefficients. It is particularly useful in combinatorics and has applications in various areas of mathematics, including generating functions and number theory.
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The binomial transform of a sequence is . When counts objects on a specified set of positions, counts the choices obtained by selecting those positions from and filling them with such an object. Its inverse is , by binomial inversion.