List questions from binomial-coefficients

Published on 03 Jun 2014 - 13:56

536

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Number of nodes with an even number of children in an ordered tree (AKA Plane Planted Tree)

Published on 30 Mar 2026 - 11:04

402

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$\sum\limits_{k=0}^{n}\binom{2n+1}{2k+1}2^{3k}$ isn't divisible by 5

Published on 30 Mar 2026 - 20:54

127

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How to simplify $F(x)=\sum_{n}^{\infty}\sum_{k}^{\infty}{n-k-1\choose k}x^n$?

Published on 30 Mar 2026 - 12:33

67

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How find this sum $\sum_{j=0}^{\infty}\binom{m+2j}{m}t^{2j},0<t<1$

Published on 09 Jun 2014 - 10:42

382

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Largest term in binomial expansion of $(1+n)^k$

Published on 10 Jun 2014 - 4:52

75

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Probability of special configuration of ones in a binary string

Published on 26 Mar 2026 - 6:28

621

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Extracting a coefficient from a generating function

Published on 30 Mar 2026 - 12:28

245

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Equality of binomial coefficients

Published on 11 Jun 2014 - 10:29

92

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Root of the polynomial $x(x-1)(x-2)\cdots(x-K)=C$

Published on 30 Mar 2026 - 12:40

439

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Generating function of binomial coefficients ${n\choose5}$

Published on 13 Jun 2014 - 8:58

71

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How prove $\sum_{k=0}^{2m}\binom{2m+1}{k}\cdot 2^k\cdot B_{k}=0$

Published on 13 Jun 2014 - 9:56

5.6k

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Prove $\sum\limits_{i=0}^n\binom{i+k-1}{k-1}=\binom{n+k}{k}$ (a.k.a. Hockey-Stick Identity)

Published on 14 Jun 2014 - 0:31

77

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Coefficient of polynomials

Published on 14 Jun 2014 - 0:52

975

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highest power of prime $p$ dividing $\binom{m+n}{n}$

Published on 30 Mar 2026 - 20:58

List Question

Closed form expression sum-product of binomials

Number of nodes with an even number of children in an ordered tree (AKA Plane Planted Tree)

$\sum\limits_{k=0}^{n}\binom{2n+1}{2k+1}2^{3k}$ isn't divisible by 5

How to simplify $F(x)=\sum_{n}^{\infty}\sum_{k}^{\infty}{n-k-1\choose k}x^n$?

How find this sum $\sum_{j=0}^{\infty}\binom{m+2j}{m}t^{2j},0<t<1$

Largest term in binomial expansion of $(1+n)^k$

Probability of special configuration of ones in a binary string

Extracting a coefficient from a generating function

Equality of binomial coefficients

Root of the polynomial $x(x-1)(x-2)\cdots(x-K)=C$

Generating function of binomial coefficients ${n\choose5}$

How prove $\sum_{k=0}^{2m}\binom{2m+1}{k}\cdot 2^k\cdot B_{k}=0$

Prove $\sum\limits_{i=0}^n\binom{i+k-1}{k-1}=\binom{n+k}{k}$ (a.k.a. Hockey-Stick Identity)

Coefficient of polynomials

highest power of prime $p$ dividing $\binom{m+n}{n}$

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