In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers { 0, 1, 2, 3, … } {\textstyle \left\{0,1,2,3,\ldots \right\}} in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities p n = ∑ k = 0 n p k p n − k. Wikipedia