[seqfan] Need help with notation: sums of subset products

[Bob Selcoe]

Hi Seqfans,

I was wondering if OEIS-style notation exists for this concept: the sum Z of the products of all combinations of numbers in set S.  Alternatively stated, the sum Z of all nonempty non-proper subset products in set S.

For example, S = {3,4,5};  Z = 3 + 4 + 5 + 3*4 + 3*5 + 4*5 + 3*4*5 = 119.

I would like to include this concept in some entries as formulas rather than as comments, so notation would be helpful. 

Thanks in advance,
Bob Selcoe