Combinatorics

We know that Î£ⁿC_r*r²= n*2^n-1 + n*(n-1)*2^n-2
(see "http://www.targetiit.com/discuss/topic/21790/solve-this-binomial-question/" for the proof)

Further we can find
Î£ⁿC_r*r³ = n*2^n-1 + 3*n(n-1)*2^n-2 + n(n-1)(n-2)*2^n-3

However on trying to find Î£ⁿC_r*r⁴,Î£ⁿC_r*r⁵ and higher powers it gets quite complicated and is tough to generalize.

Q: What is Î£ⁿC_r*r^k where 0<k<n.

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