What is the theory behind a simple pattern involving binomial coefficients?
46132
Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?
112827
Find the sum of the binomial coefficients
28737
Negative binomial coefficient
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
88059
Elementary central binomial coefficient estimates
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
101573
Subtracting even and odd binomial coefficients?
115686
A finite summation of double binomial coefficients
108401
Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
12112
What is known about the pattern for $\zeta(2n+1)$?
125220
Solving binomial theorem via induction
143509
Meaning of notation with two letters inside of parentheses [binomial coefficient]
59638
How to prove this result on binomial coefficients?
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
50662
Why does this pattern occur: $123456789 \times 8 + 9 = 987654321$
126214
Multiplying Binomial Terms
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$