Sequence factorial and its applications

In this note, we introduce sequence factorial and use this to study generalized M-bonomial coefficients. For the sequence of natural numbers, the twin concepts of sequence factorial and generalized M-bonomial coefficients, respectively, extend the corresponding concepts of factorial of an integer and binomial coefficients. Some latent properties of generalized M-bonomial coefficients by which a vast majority of practical problems involving generalized M-bonomial coefficients can be solved are derived.