In combinatorics the Eulerian number A(n, m), is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element (permutations with m "ascents"). They are the coefficients of the Eulerian polynomials:
This polynomial appears as the numerator in an expression for the generating function of the sequence 1n, 2n, 3n, ... .
Other notations for A(n, m) are E(n, m) and .
Read more about Eulerian Number: History, Basic Properties, Closed-form Expression, Summation Properties, Identities, Eulerian Numbers of The Second Kind
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