: Mathematics: Eulerian number

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Eulerian number

In combinatorics, the Eulerian number ${\ extstyle A(n,k)}$ is the number of permutations of the numbers 1 to ${\ extstyle n}$ in which exactly ${\ extstyle k}$ elements are greater than the previous element (permutations with ${\ extstyle k}$ "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Eulerian_number)

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https://en.wikipedia.org/wiki/Eulerian_number

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