一类系数依赖于两个参数的齐次递推式之解

A Formula of Solution for a Class of Homogeneous Recurrence with Two Parameters

本文拓广了文献［１］的研究范围，给出了一类依赖于两个参数的变系数递推式的解的明显表达式．有关结果，使得象Ｌａh数，两类Ｓｔｉｒｌｉｎｇ数以及置换群中的置换个数等多方面的相应定解问题，皆可以直接解出．这对具大数值双指标的递推式的计算，亦或在其理论的研究方面，都有其作用．

In this paper we consider a class of homogeneous recurrence with two parameters f (i, j)ui-p,j+g (i, j )ui-q,j-1,where i,j and q are nonnegative integers; p is positive integer; f (i,j) and g(i,j) are variablenumbers; cs(s=1, 2, …,p ) are arbitrary constants. Its general solution is given by the following formulaUi,j= {F (i,j;j-1, I) } C(i-q (j-1)-),where i,j>1, [(i-1-q (j-1))/p].