Integer Binomial Plan: a Generalization on Factorials and Binomial Coefficients

The primary goal of this paper is to achieve a simple generalization on binomial coefficients for all integer numbers and to introduce the concept of factorial n of order k, which is presented in the sets of real numbers n and integer k. Some applications of this concept are examined, featuring the consistency of its proposal, and a pair of theorems demonstrated. In generalising binomial coefficients to all integers, Pascal’s Triangle is expanded to an Integer Binomial Plan, which displays remarkable properties. Additionally, we stumble on the strange concept of semi-integer derivative of what we may call a k-derivable function