The Triplet in General. Define Coefficient of Leading Term Proper

After performing a Delta Difference operation in general, will make it possible for the coefficient of the leading term to be well defined. Which will begin a strong argument to find the nth term of a sequence of the form polynomial P(k).

Oddly enough, the unofficial Triumvirate from the Italian Peninsula - G. Cardano, S. del Ferro and N. Tartaglia kicks it all off.

Sources:

Gelfand, Gerver, Kirillov, Konstantinov and Kushnirenko - Sequences: 1969, problem 21