query: help proving an binomial identity about catalan numbers
positive_passages.docid: 145524
positive_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: 109648
negative_passages.text: Proving an identity for Bernoulli polynomials
negative_passages.docid: 1167
negative_passages.text: How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
negative_passages.docid: 35342
negative_passages.text: Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
negative_passages.docid: 36388
negative_passages.text: How to derive this Combinatorial identity
negative_passages.docid: 11335
negative_passages.text: Proving Binomial Identity without calculus
negative_passages.docid: 27141
negative_passages.text: Combinatorics identity question
negative_passages.docid: 49066
negative_passages.text: Give the combinatorial proof of the identity $\sum\limits_{i=0}^{n} \binom{k-1+i}{k-1} = \binom{n+k}{k}$
negative_passages.docid: 152084
negative_passages.text: Binomial-Theorem proof
negative_passages.docid: 103504
negative_passages.text: Weird $3^n$ in an identity to be combinatorially proved
negative_passages.docid: 154722
negative_passages.text: How do I prove $2 \binom n2 + 4 \binom n4 + 6 \binom n6 + \cdots = n 2^{n-2}$
negative_passages.docid: 1139
negative_passages.text: Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
negative_passages.docid: 27922
negative_passages.text: prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
negative_passages.docid: 139625
negative_passages.text: Proof of a Fibonacci identity
negative_passages.docid: 113290
negative_passages.text: Prove combinatorics identity
negative_passages.docid: 29828
negative_passages.text: Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
negative_passages.docid: 136580
negative_passages.text: Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$