How do you add specific elements contained within a matrix to produce a new vector?

I have the columns of n, x[n], and h[n] already produced. Now what I want to produce is the column w[n]. (Side question: is "column" correct term to be using in this instance? Or is "vertical array" or "vector" more appropriate?)

To avoid wasting your time, I've simplified the structure of w[n] in the little box there on the right-hand side, which reads: "In general, the corresponding element of w[n] meets these criteria: 1. has n+1 "component pairs", and 2. those "components pairs" are such that h[k]*x[m] where k+m=n.

Ex1. n=0. w[0] has one (0+1) "component pair:" h[0]*x[0] where k+m=0. Ex2. n=1. w[1] has two (1+1) "component pairs:" h[0]*x[1]+h[1]*x[0] where each k+m=1=n.

And in case you've now forgotten the question: How do I produce w[n] by manipulating the elements in x[n] and h[n].