One-pth Riordan Arrays in the Construction of Identities

For an integer p ≥ 2 we construct vertical and horizontal one- p th Riordan arrays from a Riordan array. When p = 2 one- p th Riordan arrays are reduced to well known half Riordan arrays. The generating functions of the A-sequences of vertical and horizontal one- p th Riordan arrays are found. The vertical and horizontal one- p th Riordan arrays provide an approach to construct many identities. They can also be used to verify some well known identities readily.