Sum of subset products

[Joe Horn]

I hope somebody here can think of an elegant way of calculating the sum of the products of all the (n-1) element subsets of an n-element set in PPL. In other words:

{A B} --> A+B
{A B C} --> AB+AC+BC
{A B C D} --> ABC+ABD+ACD+BCD
etc.

Brute force by looping is ... brutish. There must be an elegant way of doing this on the HP Prime, since it has so many list and array functions.

Thanks in advance!