To go even further, if you take the sequence A[k] = k^n and, for each n, take differences until you reach a constant, then the list A[n] of those constants is n factorial (n!).

To go even further, if you take the sequence A[k] = k^n and, for each n, take differences until you reach a constant, then the list A[n] of those constants is n factorial (n!).