query: Is the following combinatorial identity true? Is there any way to prove it?
positive_passages.docid: 18158
positive_passages.text: Inductive Proof for Vandermonde's Identity?
negative_passages.docid: 145524
negative_passages.text: Proving this identity $\sum_k\frac{1}{k}\binom{2k-2}{k-1}\binom{2n-2k+1}{n-k}=\binom{2n}{n-1}$ using lattice paths
negative_passages.docid: 24588
negative_passages.text: Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.
negative_passages.docid: 71564
negative_passages.text: Combinatorial proof of identity involving central binomial coefficients
negative_passages.docid: 959
negative_passages.text: Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
negative_passages.docid: 133150
negative_passages.text: Fibonacci combinatorial identity: $F_{2n} = {n \choose 0} F_0 + {n\choose 1} F_1 + ... {n\choose n} F_n$
negative_passages.docid: 45204
negative_passages.text: Combinatorial proofs: having a difficult time understanding how to write them out
negative_passages.docid: 27585
negative_passages.text: Combinatorial proof of Stirling Number Identity (First Kind)
negative_passages.docid: 110441
negative_passages.text: Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
negative_passages.docid: 120074
negative_passages.text: Prove by Combinatorial Argument that $\binom{n}{k}= \frac{n}{k} \binom{n-1}{k-1}$
negative_passages.docid: 105237
negative_passages.text: Alternating sum of binomial coefficients identity
negative_passages.docid: 9522
negative_passages.text: Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
negative_passages.docid: 74730
negative_passages.text: Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
negative_passages.docid: 10875
negative_passages.text: proof of binomial identity involving double sum
negative_passages.docid: 42062
negative_passages.text: Interpretation of a combinatorial expression
negative_passages.docid: 56828
negative_passages.text: A combinatorial proof that the alternating sum of binomial coefficients is zero