Exactly. The other perspective: When you see 'difference', think 'derivative' . Approximately, what the difference table is doing is differentiating until the

Exactly. The other perspective: When you see 'difference', think 'derivative' . Approximately, what the difference table is doing is differentiating until the leading term is constant. If we end up with a constant k levels down, we must have had a.x^k in the polynomial, as the derivative of a.x^k = ak.x^(k-1). Repeating this k times gives constant = a.k! So the leading coefficient of the polynomial, a = constant/k! I guess the next step is to subtract the values generated by this term from the sequence, then repeat to find the next term in the polynomial...