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Eulerian number
Number of permutations of the numbers from 1 to n in which m elements are greater than the previous element
In combinatorics, the Eulerian number A ( n , k ) {\textstyle A(n,k)} is the number of permutations of the numbers 1 to n {\textstyle n} in which exactly k {\textstyle k} elements are greater than the previous element (permutations with k {\textstyle k} "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis.
From Wikipedia
In combinatorics, the Eulerian number A ( n , k ) {\textstyle A(n,k)} is the number of permutations of the numbers 1 to n {\textstyle n} in which exactly k {\textstyle k} elements are greater than the previous element (permutations with k {\textstyle k} "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis. Other notations for A ( n , k ) {\textstyle A(n,k)} are E ( n , k ) {\textstyle E(n,k)} and ⟨ n k ⟩ {\displaystyle \textstyle \left\langle {n \atop k}\right\rangle } .
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