Sum involving binomial coefficients - generalisation of hockey stick identity?
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
127150
Finding general formula of $\sum_{i=0}^n i^2 \binom{n}{i}$
52557
Derivation of binomial coefficient in binomial theorem.
144571
A conjecture including binomial coefficients
143945
Summation of combination of binomial coefficient
99249
Sum of product of binomial coefficients: $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{n + k}{k} = (-1)^n$
56828
A combinatorial proof that the alternating sum of binomial coefficients is zero
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
56138
Proving $\sum_{k=0}^{2m}(-1)^k{\binom{2m}{k}}^3=(-1)^m\binom{2m}{m}\binom{3m}{m}$ (Dixon's identity)
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
45672
Even/Odd Binomial Coefficients
7143
Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$
91239
Sum of binomial coefficients involving $n,p,q,r$
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
42606
Orthogonality for Binomial Coefficients
105237
Alternating sum of binomial coefficients identity