How do I go about approaching the following problem?
$$\sum_{k=1}^n k^2 C(n,k) = n(n+1)2^{n-2}$$
I don't know how to interpret the summation of something combinatorially, especially with a k^2 term. Any help or tips would be greatly appreciated!
2026-03-30 02:04:49.1774836289
Combinatorial Proofs with Summation on One Side
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The combinatorial proof: Given $n$ people, choose a committee of size $k$, then choose a chairperson and a vice chair person (possibly the same person) ... This the LHS.
Another way ... if the the chair & vice are the same person $n2^{n-1}$ ... & if the are different $n(n-1) 2^{n-2}$ ... add these, this is the RHS.