List questions from binomial-coefficients

Published on 13 Apr 2026 - 3:02

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$n_{p,k} = \frac{1}{p}\binom{p}{k}$ for counting $k$-element subsets of $\left\{1,2,\ldots,p\right\}$ with sum divisible by $p$

Published on 16 Apr 2026 - 12:44

84

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How can I show that $\sum_{k=0}^n [\frac{(n-2k)}{n}{n \choose k}]^2 = \frac{2}{n}{2n - 2 \choose n - 1}$?

Published on 15 Apr 2026 - 5:41

253

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Binomial Coefficient Identity, Double Series, Floor Function

Published on 12 Apr 2026 - 2:59

824

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What is the distribution of 2 consecutive Binomial trials?

Published on 10 Apr 2026 - 6:03

3.9k

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How often can a number occur in Pascals Triangle?

Published on 08 Apr 2026 - 21:30

53

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Binomial Coefficients proof

Published on 15 Apr 2026 - 13:27

2.9k

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derivative of binomial probability

Published on 13 Apr 2026 - 6:59

325

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sum of squares of diagonal binomial coefficients.

Published on 12 Apr 2026 - 12:07

450

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Prove that $k\binom{n}{k}=n\binom{n-1}{k-1}$

Published on 14 Apr 2026 - 6:37

107

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Finding value of $\left \lfloor \frac{2017!}{2016!+2015!+\cdots \cdots + 2!+1!}\right\rfloor $

Published on 16 Apr 2026 - 11:07

2.1k

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Induction proof (combinatorics): $\sum_{k=0}^{n}{n\choose k}{k\choose m} = {n\choose m}2^{n-m}$

Published on 17 Apr 2026 - 14:12

489

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Binomial coefficient notated by recursive summations

Published on 17 Apr 2026 - 8:51

105

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Proof of equation with nested, dependent integrals

Published on 09 Apr 2026 - 4:39

141

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Is there a simpler (preferably closed-form) way to compute this sum of binomial coefficients?

Published on 14 Apr 2026 - 2:35

List Question

Stirling's Formula for Binomial Coefficient

$n_{p,k} = \frac{1}{p}\binom{p}{k}$ for counting $k$-element subsets of $\left\{1,2,\ldots,p\right\}$ with sum divisible by $p$

How can I show that $\sum_{k=0}^n [\frac{(n-2k)}{n}{n \choose k}]^2 = \frac{2}{n}{2n - 2 \choose n - 1}$?

Binomial Coefficient Identity, Double Series, Floor Function

What is the distribution of 2 consecutive Binomial trials?

How often can a number occur in Pascals Triangle?

Binomial Coefficients proof

derivative of binomial probability

sum of squares of diagonal binomial coefficients.

Prove that $k\binom{n}{k}=n\binom{n-1}{k-1}$

Finding value of $\left \lfloor \frac{2017!}{2016!+2015!+\cdots \cdots + 2!+1!}\right\rfloor $

Induction proof (combinatorics): $\sum_{k=0}^{n}{n\choose k}{k\choose m} = {n\choose m}2^{n-m}$

Binomial coefficient notated by recursive summations

Proof of equation with nested, dependent integrals

Is there a simpler (preferably closed-form) way to compute this sum of binomial coefficients?

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