List questions from binomial-coefficients

Published on 21 Dec 2014 - 15:09

97

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If $k, m, n$, are natural numbers and $k \leq n$ What is the final answer of this :

Published on 29 Mar 2026 - 10:08

69

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Congruence with binomial

Published on 26 Mar 2026 - 17:28

431

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How to prove that the sum of squared binomials equals $\binom{2n}{n}$

Published on 22 Dec 2014 - 19:45

485

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Binomial theorem.

Published on 23 Dec 2014 - 18:35

80

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expressing canonical base of univariate polynomials in binomial base

Published on 24 Dec 2014 - 8:35

129

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Asymptotics of integer compositions

Published on 24 Dec 2014 - 10:54

174

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An identity involving partial fractions decompositions

Published on 27 Mar 2026 - 1:44

485

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Good approximation for $\binom{N}{\frac{N}{2}}$

Published on 30 Mar 2026 - 9:29

478

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What is the value of $\sum_{n=0}^{\infty}(-\frac{1}{8})^n\binom{2n}{n}$

Published on 25 Dec 2014 - 14:57

81

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If a word appears with probability $0.05$, how many words are needed so that it appears with probability $0.99$?

Published on 25 Dec 2014 - 23:29

627

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How to compute $\sum^n_{k=0}(-1)^k\binom{n}{k}k^n$

Published on 26 Dec 2014 - 4:19

1.3k

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Xmas Maths 2014

Published on 03 Apr 2026 - 1:41

1.3k

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Combinatoric proof for $\sum_{k=0}^n{n\choose k}\left(-1\right)^k\left(n-k\right)^4 = 0$ ($n\geqslant5$)

Published on 26 Mar 2026 - 11:18

356

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Is there a "counting groups/committees" proof for the identity $\binom{\binom{n}{2}}{2}=3\binom{n+1}{4}$?

Published on 26 Mar 2026 - 11:17

List Question

Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of

If $k, m, n$, are natural numbers and $k \leq n$ What is the final answer of this :

Congruence with binomial

How to prove that the sum of squared binomials equals $\binom{2n}{n}$

Binomial theorem.

expressing canonical base of univariate polynomials in binomial base

Asymptotics of integer compositions

An identity involving partial fractions decompositions

Good approximation for $\binom{N}{\frac{N}{2}}$

What is the value of $\sum_{n=0}^{\infty}(-\frac{1}{8})^n\binom{2n}{n}$

If a word appears with probability $0.05$, how many words are needed so that it appears with probability $0.99$?

How to compute $\sum^n_{k=0}(-1)^k\binom{n}{k}k^n$

Xmas Maths 2014

Combinatoric proof for $\sum_{k=0}^n{n\choose k}\left(-1\right)^k\left(n-k\right)^4 = 0$ ($n\geqslant5$)

Is there a "counting groups/committees" proof for the identity $\binom{\binom{n}{2}}{2}=3\binom{n+1}{4}$?

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