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!).
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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!).