Double 3-dimensional riordan arrays and their applications

Abstract

In this paper, we give the group of double 3-dimensional Riordan arrays. Also we examine new sums involving Fibonacci numbers and special numbers, using combinatorial identities and the double 3-dimensional Riordan arrays. For instance, for non-negative integer n, n X l=0 n-l X k =0 n X j =0 +l (-1)l+j dk+l n+l-jdl+k j (n-j +l)!j! n X= Fn and l=0 n-l X k =0 n-k-l X j =0 (-1)jdldkj Hk+2 n-k-l-j l!j! =Hn2, where drn, Fn and Hrn are r-derangement number, Fibonacci number and hyperharmonic number of order respectively.