List questions from binomial-coefficients

Published on 26 Mar 2026 - 6:21

108

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Evaluate the sum $\sum_{0\leq j < k\leq n}\binom{n}{j}\binom{n}{k}$

Published on 16 May 2014 - 3:25

378

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Proving $\sum_{k=1}^{n}\binom{n-1}{k-1}{\binom{n+k}{k}}^{-1}=\frac 12$ combinatorially

Published on 17 May 2014 - 9:02

109

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How find this sum $\sum_{k=0}^{p}t^k\binom{n}{k}\binom{m}{p-k}$

Published on 19 May 2014 - 12:14

3.2k

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How do you calculate a binomial distribution with k > R as opposed to k = R

Published on 28 Mar 2026 - 10:04

1.1k

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Binomial Sum Related to Fibonacci: $\sum\binom{n-i}j\binom{n-j}i=F_{2n+1}$

Published on 27 Mar 2026 - 6:12

216

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An inverse binomial summation.

Published on 19 May 2014 - 18:28

1.9k

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Integral with binomial coefficient

Published on 22 May 2014 - 5:33

386

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How find this sum $ \frac{1}{1999}\binom{1999}{0}-\frac{1}{1998}\binom{1998}{1}+\cdots-\frac{1}{1000}\binom{1000}{999}$

Published on 23 May 2014 - 12:33

211

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Sum of products of binomial coefficient $-1/2 \choose x$

Published on 23 May 2014 - 12:15

72

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Prove the following :

Published on 30 Mar 2026 - 15:11

213

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Binomial Theorem on a Ring with Order 2

Published on 28 Mar 2026 - 10:03

462

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Does $\sum_{k=0}^{k=n} {n \choose k} k!$ have a closed form for integers $k,n$?

Published on 24 May 2014 - 3:45

205

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Binomial Expression

Published on 24 May 2014 - 4:58

204

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Binomial coefficient proof

Published on 28 Mar 2026 - 10:03

List Question

Combinatorial proof of $n! = {n\choose k}k!(n-k)!$

Evaluate the sum $\sum_{0\leq j < k\leq n}\binom{n}{j}\binom{n}{k}$

Proving $\sum_{k=1}^{n}\binom{n-1}{k-1}{\binom{n+k}{k}}^{-1}=\frac 12$ combinatorially

How find this sum $\sum_{k=0}^{p}t^k\binom{n}{k}\binom{m}{p-k}$

How do you calculate a binomial distribution with k > R as opposed to k = R

Binomial Sum Related to Fibonacci: $\sum\binom{n-i}j\binom{n-j}i=F_{2n+1}$

An inverse binomial summation.

Integral with binomial coefficient

How find this sum $ \frac{1}{1999}\binom{1999}{0}-\frac{1}{1998}\binom{1998}{1}+\cdots-\frac{1}{1000}\binom{1000}{999}$

Sum of products of binomial coefficient $-1/2 \choose x$

Prove the following :

Binomial Theorem on a Ring with Order 2

Does $\sum_{k=0}^{k=n} {n \choose k} k!$ have a closed form for integers $k,n$?

Binomial Expression

Binomial coefficient proof

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