List questions from binomial-coefficients

Published on 27 Mar 2026 - 23:35

129

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Sum involving binomial coefficients and falling factorials

Published on 15 Jan 2019 - 3:15

274

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Binomial sum which adds to $2^n n!$

Published on 25 Mar 2026 - 20:52

423

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Find the sum $S=\sum\limits_{k=1}^{n} {4k-1 \choose k}$

Published on 16 Jan 2019 - 5:26

473

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Summation of: (binomial coefficients * Stirling numbers of the second kind)

Published on 26 Mar 2026 - 12:37

30

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Analytical form of the binomial moments

Published on 17 Jan 2019 - 16:07

329

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Prove for any positive integer $n$, $(4n)!$ is divisible by $2^{3n}\cdot 3^n$

Published on 27 Mar 2026 - 13:27

177

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Finding determinant of matrix involving binomial coefficients

Published on 17 Jan 2019 - 18:59

183

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Summation of Stirling numbers of second kind

Published on 26 Mar 2026 - 12:36

302

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Evaluate $4^n = \sum_{k=0}^{n} {n \choose k} 3^k$

Published on 25 Mar 2026 - 20:52

241

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Lucas number identity

Published on 25 Mar 2026 - 20:24

52

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Summation using binomial theorem

Published on 27 Mar 2026 - 10:30

424

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Closed form for product of Stirling numbers of the second kind

Published on 26 Mar 2026 - 12:37

532

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Closed form expression for the harmonic sum $\sum\limits_{n=1}^{\infty}\frac{H_{2n}}{n^2\cdot4^n}{2n \choose n}$

Published on 25 Mar 2026 - 9:28

152

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How to prove combinatorial $\sum_{k=0}^{n/2} {n\choose2k} = \sum_{k=0}^{n/2 - 1} {n\choose2k+1} = 2^{n-1}$

Published on 24 Jan 2019 - 11:04

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Is there some way to prove $n\binom nr=(r+1)\binom n{r+1}+r\binom nr$ using generating functions?

Sum involving binomial coefficients and falling factorials

Binomial sum which adds to $2^n n!$

Find the sum $S=\sum\limits_{k=1}^{n} {4k-1 \choose k}$

Summation of: (binomial coefficients * Stirling numbers of the second kind)

Analytical form of the binomial moments

Prove for any positive integer $n$, $(4n)!$ is divisible by $2^{3n}\cdot 3^n$

Finding determinant of matrix involving binomial coefficients

Summation of Stirling numbers of second kind

Evaluate $4^n = \sum_{k=0}^{n} {n \choose k} 3^k$

Lucas number identity

Summation using binomial theorem

Closed form for product of Stirling numbers of the second kind

Closed form expression for the harmonic sum $\sum\limits_{n=1}^{\infty}\frac{H_{2n}}{n^2\cdot4^n}{2n \choose n}$

How to prove combinatorial $\sum_{k=0}^{n/2} {n\choose2k} = \sum_{k=0}^{n/2 - 1} {n\choose2k+1} = 2^{n-1}$

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