A generalization of the Eulerian numbers with a probabilistic application. (English) Zbl 0801.60013
Summary: We study a generalization of the Eulerian numbers and a class of polynomials related to them. An interesting application to probability theory is given in Section 3. There we use these extended Eulerian numbers to construct an uncountably infinite family of lattice random variables whose first \(n\) moments coincide with the first \(n\) moments of the sum of \(n+1\) uniform random variables. A number of combinatorial identities are also deduced.
Online Encyclopedia of Integer Sequences:
Triangle T(n,k) read by rows: T(n,k) = Sum_{j=0..k} (-1)^j *binomial(n+1,j)*(k+2-j)^n, 0 <= k < n.References:
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