On the Generalization of Factoriangular Numbers

A factoriangularnumber is a sum of a factorial and its corresponding triangular number. This paper presents some forms of the generalization of factoriangular numbers. One generalization is the ()mn-factoriangular number which is of the form (n!)m+Sm(n), where (n!)mis the mth power of the factorial of nand Sm(n)is the sum of the m-powers of n. This generalized form is explored for the different values of the natural number m. The investigation results to some interesting proofs of theorems related thereto.