On a Family of Generalized Pascal Triangles Defined by Exponential Riordan Arrays
On a Family of Generalized Pascal Triangles Defined by Exponential Riordan Arrays
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发表时间：
2007-03
影响因子：
0.5
通讯作者：
P. Barry
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作者：
P. Barry
我们引入了一类由指数Riordan数组定义的数字三角形，它推广了Pascal三角形。我们刻画了这些三角形的行和和中心系数，并定义和研究了一组广义加泰罗尼亚数。我们建立了与Hermite， Laguerre和Bessel多项式的链接，以及与Narayana和Lah数的链接。
We introduce a family of number triangles defined by exponential Riordan arrays, which generalize Pascal’s triangle. We characterize the row sums and central coefficients of these triangles, and define and study a set of generalized Catalan numbers. We establish links to the Hermite, Laguerre and Bessel polynomials, as well as links to the Narayana and Lah numbers.