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Combinatorial interpretation of identity: $\sum\limits_{j=0}^b\binom{b}{j}^2\binom{n+j}{2b}=\binom{n}{b}^2$

Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$ [duplicate]

What is the combinatorial interpretation behind the recursive relation: $L(n,k+1)=\frac{n-k}{k\left(k+1\right)}L(n,k)$

Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$

How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?

Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$

Combinatorially prove that $\sum_{i=0}^n {n \choose i} 2^i = 3^n $

Help with combinatorial proof of binomial identity: $\sum\limits_{k=1}^nk^2{n\choose k}^2 = n^2{2n-2\choose n-1}$

How to begin combinatorial proof of $\sum_{k=1}^n k \binom nk^2 = n \binom{2n-1}{n-1}$

Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$

Combinatorial proof that binomial coefficients are given by alternating sums of squares?

Let $a_n$ be the position of the nth $1$in the string $t_n$. Prove that: $a_n = [\frac{1+\sqrt5}{2} . n]$

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Combinatorial proof that $\frac{({10!})!}{{10!}^{9!}}$ is an integer [duplicate]

Combinatorial proof of identity involving central binomial coefficients

How do I prove this combinatorial identity

Combinatorial proof of a binomial coefficient summation.

New posts in combinatorial-proofs

Combinatorial proof for Stirling number of 1st kind's generating function [duplicate]

Catalan numbers: bijection between applications of a binary operator and Dyck words.

Combinatorial proof for $\sum_{r=0} {n \choose {2r}} = \sum_{r=0} {n \choose {2r+1}} = 2^{n-1}$

Combinatorial interpretation of identity: $\sum\limits_{j=0}^b\binom{b}{j}^2\binom{n+j}{2b}=\binom{n}{b}^2$

Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$ [duplicate]

What is the combinatorial interpretation behind the recursive relation: $L(n,k+1)=\frac{n-k}{k\left(k+1\right)}L(n,k)$

Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$

How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?

Proof Binomial Coefficient Identity: $\sum_{k=0}^n\frac{k k!}{n^k}\binom{n}{k}=n$

Combinatorially prove that $\sum_{i=0}^n {n \choose i} 2^i = 3^n $

Help with combinatorial proof of binomial identity: $\sum\limits_{k=1}^nk^2{n\choose k}^2 = n^2{2n-2\choose n-1}$

How to begin combinatorial proof of $\sum_{k=1}^n k \binom nk^2 = n \binom{2n-1}{n-1}$

Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$

Combinatorial proof that binomial coefficients are given by alternating sums of squares?

Let $a_n$ be the position of the nth $1$in the string $t_n$. Prove that: $a_n = [\frac{1+\sqrt5}{2} . n]$

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Combinatorial proof that $\frac{({10!})!}{{10!}^{9!}}$ is an integer [duplicate]

Combinatorial proof of identity involving central binomial coefficients

How do I prove this combinatorial identity

Combinatorial proof of a binomial coefficient summation.