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arildno

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Hi there!

I am seeking a nice formula for the following function S(k,n), k and n natural numbers, k<=n, where S(k,n) is the sum of all possible products (permutations not allowed) of k distinct integers, where the integer set runs from 1 to n.

Thus, for example, we have the trivial cases of S(1,n)=n(n+1)/2 and S(n,n)=n!

Thanks in advance

EDIT:

I'm not really interested in an implicit recursive method (that's fairly trivial to set up), but an explicit expression of S

I am seeking a nice formula for the following function S(k,n), k and n natural numbers, k<=n, where S(k,n) is the sum of all possible products (permutations not allowed) of k distinct integers, where the integer set runs from 1 to n.

Thus, for example, we have the trivial cases of S(1,n)=n(n+1)/2 and S(n,n)=n!

Thanks in advance

EDIT:

I'm not really interested in an implicit recursive method (that's fairly trivial to set up), but an explicit expression of S

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