Backgammon Array Mapping

A friend of yours is working on an AI program to play backgammon, and she has a small problem. At the end of the game, each player's $15$ pieces are moved onto a set of $6$ board positions called points, numbered $1$ through $6$. The pieces can be distributed in any manner across these points: all $15$ could be on point $3$; $5$ could be on point $6$, $2$ on point $5$, $3$ on point $4$ and $5$ on point $2$; etc. Your friend wants to store all these possible configurations (of which there are $15504$) into a linear array, but she needs a mapping from configuration to array location. It seems logical that the configuration with all $15$ pieces on point $1$ should correspond to array location $0$, and the configuration of all $15$ pieces on point $6$ should correspond to the last array location. It's the ones in between that are giving her problems. That's why she has come to you.

You decide to specify a configuration by listing the number of pieces on each point, starting with point $6$. For example, the two configurations described above could be represented by (0, 0, 0, 15, 0, 0) and (5, 2, 3, 0, 5, 0). Then you can order the configurations in lexicographic ordering, starting with (0, 0, 0, 0, 0, 15), then (0, 0, 0, 0, 1, 14), (0, 0, 0, 0, 2, 13), ..., (0, 0, 0, 0, 14, 1), (0, 0, 0, 0, 15, 0), (0, 0, 0, 1, 0, 14), (0, 0, 0, 1, 1, 13) etc., ending with (15, 0, 0, 0, 0, 0). Now all you need is a way to map these orderings to array indices. Literally, that's all you need, because that's what this problem is all about.