Generalized Factoriangular Numbers And Factoriangular Triangles

A factoriangular number is defined as the sum of corresponding factorial and triangular number. This paper aims to generalize this number as sum of any factorial and any triangular number and explore such generalization. This study is a basic research in number theory that uses mathematical exposition and exploration. The generalized factoriangular number is of the form where is the factorial of a natural number and is the triangular number. When the sum is an ordinary factoriangular number. A consequence of the generalization is the creation of interesting Pascal-like triangles that are hereby called factoriangular triangles and formation of their corresponding integer sequences. Generalized factoriangular numbers and factoriangular triangles can be utilized as recreational mathematics for students. Further generalizations of factoriangular number and expositions on factoriangular triangles can be done next.