Question

A combinatorial solution to $\sum_{i=1}^n \binom ni i^4$

score 74 · Answer 1 · 2021-05-13 09:22:04

74

Views

A combinatorial solution to $\sum_{i=1}^n \binom ni i^4$

Published on 13 May 2021 - 9:22

score 146 · Answer 2 · 2021-05-14 20:46:54

146

Views

Prove that $\varphi (v,\cdots, v)=\sum _{|\alpha |=k}\frac{k!}{\alpha !}v^\alpha \varphi^\alpha $

Published on 14 May 2021 - 20:46

score 127 · Answer 3 · 2021-05-27 01:05:55

127

Views

Summation involving three indices and combinations: How I can prove the next equality?

Published on 27 May 2021 - 1:05

score 186 · Answer 4 · 2026-03-29 03:53:16

186

Views

A serious Glitch in my combinatorial proof of a recursive identity to count tilings of an $n$ board by squares and dominos

Published on 29 Mar 2026 - 3:53

score 41 · Answer 5 · 2021-05-29 13:31:12

41

Views

A very basic combinatorial question.

Published on 29 May 2021 - 13:31

score 209 · Answer 6 · 2021-05-31 01:13:03

209

Views

Finding combinatorial proof of log concavity of certain sequence of binomial coefficients

Published on 31 May 2021 - 1:13

score 306 · Answer 7 · 2021-06-02 06:54:37

306

Views

(combinatorial and algebraic) proof that $\sum_{q=1}^n \binom{n}{q}\binom{n-q}{2k-2q}2^{2(k-q)} = \binom{2n}{2k} - \binom{n}{2k}2^{2k}$

Published on 02 Jun 2021 - 6:54

score 218 · Answer 8 · 2021-06-04 10:01:14

218

Views

Prove combinatorically $ \sum_{k=1}^{n} k^2 = n{n+1 \choose 2} - {n+1 \choose 3 } $

Published on 04 Jun 2021 - 10:01

score 80 · Answer 9 · 2021-06-04 10:43:15

80

Views

Proof that $\frac {(2n)!}{n! 2^n}$ is integer

Published on 04 Jun 2021 - 10:43

score 89 · Answer 10 · 2021-06-09 03:03:41

89

Views

Explicit injective generalization of map $\mathbb{N}\times\mathbb{N}\to \mathbb{N}$

Published on 09 Jun 2021 - 3:03

score 42 · Answer 11 · 2021-06-09 04:04:32

42

Views

Injective map from cross product of to the collection of perfect squares to $\mathbb{N}$

Published on 09 Jun 2021 - 4:04

score 143 · Answer 12 · 2021-06-13 12:26:35

143

Views

Wikipedia combinatorial proof of Fermat's little theorem

Published on 13 Jun 2021 - 12:26

score 220 · Answer 13 · 2021-06-15 08:50:57

220

Views

Explicit map from $\mathbb{N}^t \to \mathbb{N}$

Published on 15 Jun 2021 - 8:50

score 173 · Answer 14 · 2021-06-16 12:32:52

173

Views

Simplifying a summation with binomial coefficients

Published on 16 Jun 2021 - 12:32

score 333 · Answer 15 · 2026-03-25 09:28:33

333

Views

Combinatorial interpretation of $\frac{1}{1-e^{x+1}}$ or $\frac{1}{1-e^{x-1}}$

Published on 25 Mar 2026 - 9:28

List Question

A combinatorial solution to $\sum_{i=1}^n \binom ni i^4$

Prove that $\varphi (v,\cdots, v)=\sum _{|\alpha |=k}\frac{k!}{\alpha !}v^\alpha \varphi^\alpha $

Summation involving three indices and combinations: How I can prove the next equality?

A serious Glitch in my combinatorial proof of a recursive identity to count tilings of an $n$ board by squares and dominos

A very basic combinatorial question.

Finding combinatorial proof of log concavity of certain sequence of binomial coefficients

(combinatorial and algebraic) proof that $\sum_{q=1}^n \binom{n}{q}\binom{n-q}{2k-2q}2^{2(k-q)} = \binom{2n}{2k} - \binom{n}{2k}2^{2k}$

Prove combinatorically $ \sum_{k=1}^{n} k^2 = n{n+1 \choose 2} - {n+1 \choose 3 } $

Proof that $\frac {(2n)!}{n! 2^n}$ is integer

Explicit injective generalization of map $\mathbb{N}\times\mathbb{N}\to \mathbb{N}$

Injective map from cross product of to the collection of perfect squares to $\mathbb{N}$

Wikipedia combinatorial proof of Fermat's little theorem

Explicit map from $\mathbb{N}^t \to \mathbb{N}$

Simplifying a summation with binomial coefficients

Combinatorial interpretation of $\frac{1}{1-e^{x+1}}$ or $\frac{1}{1-e^{x-1}}$

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