Trinomial Coefficients and Kings

Trinomial Coefficients and Kings

The term trinomial coefficient is used a couple different ways. The most natural use of the term is a generalization of bionomial coefficients to three variables, i.e. numbers of the form where i + j + k = n. These numbers are the coefficients of yj zk in the expansion of (x + y + z)n. But there’s another use of the term trinomial coefficient, the one that we are interest in for this post, and that is the coefficients of xk in the expansion of (…