Math Help - Help needed on sum of product combinations

Does anyone know how to calculate a sum of all i-element product combinations from a k-element set of ordered natural numbers say {n,n-1,..,n-k+1}. I mean how to express it in a hopefully short equation rather than doing it manually. If we denote this sum by S_i^k(n) then an example of such sum S_2^4(6)=
3*4+3*5+3*6+4*5+4*6+5*6.

which is a sum of all 2 element products from the 4-element set of natural numbers ending on 6: {3 4 5 6}.

Help would be greatly appreciated and would help to solve distibution of a real problem in telecommunication industry

Best