Polynomial sequence

In mathematics, a polynomial sequence is a sequence of polynomials indexed by the nonnegative integers 0, 1, 2, 3, ..., in which each index is equal to the degree of the corresponding polynomial. Polynomial sequences are a topic of interest in enumerative combinatorics and algebraic combinatorics, as well as applied mathematics.
Examples.
Some polynomial sequences arise in physics and approximation theory as the solutions of certain ordinary differential equations:
Others come from statistics:
Many are studied in algebra and combinatorics: