List questions from binomial-coefficients

Published on 05 May 2020 - 21:48

426

Views

show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

Published on 27 Mar 2026 - 7:16

71

Views

$ \lim_{n\to \infty} \sum_{k=0}^n \frac {\binom{n}{k}}{(n^k)(k+3)}$

Published on 07 May 2020 - 2:41

139

Views

Show $\sum_{k=0}^{n} \binom{n}{k} \binom{r+k}{n} =\sum_{k=0}^{n} (-1)^{n-k} \binom{n}{k} \binom{r+k}{k} 2^k$?

Published on 07 May 2020 - 12:56

135

Views

Stirling Numbers of first kind $s(n,k)$

Published on 27 Mar 2026 - 2:35

73

Views

Comparing a binomial coefficient to a fraction of factorials

Published on 07 Apr 2026 - 16:33

261

Views

Combinatorial proof of $\sum_{k=n}^{q-m} \binom{k}{n} \binom{q-k}{m} = \binom{q+1}{m+n+1}$

Published on 27 Mar 2026 - 7:17

68

Views

How to prove two binomial expressions are equivalent?

Published on 08 May 2020 - 10:28

164

Views

A certain sum of products of binomial coefficients

Published on 28 Mar 2026 - 12:49

98

Views

Trying to understand a proof of Fleck congruence

Published on 08 May 2020 - 22:53

189

Views

Calculating $\sum_{k=0}^{n}\binom{n}{k}\frac{1}{k+1}$

Published on 30 Mar 2026 - 11:22

62

Views

How can we compute a binomial series of the form $\sum_{n=0}^\infty {-{3}/{2} \choose n}\frac{(-1)^n}{(2n+1)^3}$

Published on 09 May 2020 - 17:40

77

Views

On Hilbert polynomials

Published on 09 May 2020 - 22:30

50

Views

What is a closed form for this combinatorial sum?

Published on 26 Mar 2026 - 19:37

104

Views

Evaluating: $\lim_{x\to\infty} \frac{\sum_{k=0}^{x/2}\binom{x}{2k}2k(x-2k)}{\sum_{k=0}^{x/2}\binom{x}{2k}(x-2k)^{2}}$

Published on 10 May 2020 - 18:15

List Question

Calculating minimum points to pass as a team in a sport league

show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

$ \lim_{n\to \infty} \sum_{k=0}^n \frac {\binom{n}{k}}{(n^k)(k+3)}$

Show $\sum_{k=0}^{n} \binom{n}{k} \binom{r+k}{n} =\sum_{k=0}^{n} (-1)^{n-k} \binom{n}{k} \binom{r+k}{k} 2^k$?

Stirling Numbers of first kind $s(n,k)$

Comparing a binomial coefficient to a fraction of factorials

Combinatorial proof of $\sum_{k=n}^{q-m} \binom{k}{n} \binom{q-k}{m} = \binom{q+1}{m+n+1}$

How to prove two binomial expressions are equivalent?

A certain sum of products of binomial coefficients

Trying to understand a proof of Fleck congruence

Calculating $\sum_{k=0}^{n}\binom{n}{k}\frac{1}{k+1}$

How can we compute a binomial series of the form $\sum_{n=0}^\infty {-{3}/{2} \choose n}\frac{(-1)^n}{(2n+1)^3}$

On Hilbert polynomials

What is a closed form for this combinatorial sum?

Evaluating: $\lim_{x\to\infty} \frac{\sum_{k=0}^{x/2}\binom{x}{2k}2k(x-2k)}{\sum_{k=0}^{x/2}\binom{x}{2k}(x-2k)^{2}}$

Trending Questions

Popular # Hahtags

Popular Questions