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# Deduce this combinatorial summation formula watch

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1. I am working on a combinatorial summation problem (please see the attached file).

In my Combinatorics lectures, we studied a theorem relating to orthogonality for binomial coefficients. This is what the first sentence of the problem relates to.

I have managed to solve the first part of the question (finding the Stirling number). However, I am unsure how to solve the very last part of the problem (which requires a deduction).
I would greatly appreciate a HINT(S) as to how to solve this last part of the problem.
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2. (Original post by CKKOY)
I am working on a combinatorial summation problem (please see the attached file).

In my Combinatorics lectures, we studied a theorem relating to orthogonality for binomial coefficients. This is what the first sentence of the problem relates to.

I have managed to solve the first part of the question (finding the Stirling number). However, I am unsure how to solve the very last part of the problem (which requires a deduction).
I would greatly appreciate a HINT(S) as to how to solve this last part of the problem.
Not really my area, but wikipedia suggests that there is a formula

that looks like you can punch around to get the result that you require. Did this arise in the bits of the question you've done already?
3. Thank you for the reply. Yes, it did come up in the other parts of the question.

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Updated: November 7, 2015
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