Question

Proving $\sum_{k=0}^{n}\left(\sum_{l=0}^{k}\binom{n}{k}\binom{k}{l} l\right)=n \times 3^{n-1}$ with a combinatoric argument

score 188 · Answer 1 · 2020-11-03 21:22:24

188

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Proving $\sum_{k=0}^{n}\left(\sum_{l=0}^{k}\binom{n}{k}\binom{k}{l} l\right)=n \times 3^{n-1}$ with a combinatoric argument

Published on 03 Nov 2020 - 21:22

score 127 · Answer 2 · 2020-11-05 04:56:40

127

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infinite sum of inverse binomial coefficient encountered in Bayesian treatment of the German tank problem

Published on 05 Nov 2020 - 4:56

score 208 · Answer 3 · 2020-11-12 19:17:49

208

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How many possible Barcodes are there of width $12$?

Published on 12 Nov 2020 - 19:17

score 61 · Answer 4 · 2020-11-15 02:32:21

61

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Combinatorial Proof of $|T| \leq 2 \binom{n}{\lfloor n/2 \rfloor}$

Published on 15 Nov 2020 - 2:32

score 155 · Answer 5 · 2020-11-16 04:17:03

155

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Combinatoric Proof to show the number of good vectors is at most $\binom{n}{\lfloor n/2 \rfloor}$

Published on 16 Nov 2020 - 4:17

score 147 · Answer 6 · 2026-03-29 04:11:09

147

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Interesting question about exponential generating function of the number of partitions under a certain statistic.

Published on 29 Mar 2026 - 4:11

score 105 · Answer 7 · 2020-11-23 05:50:00

105

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prove the identity $\sum_{k=0}^n {s+k \choose k}{n-k \choose m} = {s+n+1 \choose s+m+1} $

Published on 23 Nov 2020 - 5:50

score 143 · Answer 8 · 2020-11-23 08:20:49

143

Views

Proving identity through combinatorial model

Published on 23 Nov 2020 - 8:20

score 86 · Answer 9 · 2020-11-23 13:20:37

86

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Find the value of $\frac{\sum_{k<\frac n2} (n-2k){n \choose k}}{2^n-1}$

Published on 23 Nov 2020 - 13:20

score 51 · Answer 10 · 2020-11-24 05:35:43

51

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Number of independent functions for 3 bit strings

Published on 24 Nov 2020 - 5:35

score 453 · Answer 11 · 2020-11-24 17:40:02

453

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Can this be proved using Combinatorics or generating functions?

Published on 24 Nov 2020 - 17:40

score 76 · Answer 12 · 2020-11-25 17:09:59

76

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How would I prove $\sum_{p=1}^{n}\binom{n}{p}p^m(-1)^p=0, m \in \mathbb{N}, 1\leq m < n $ via induction?

Published on 25 Nov 2020 - 17:09

score 133 · Answer 13 · 2020-11-27 15:34:22

133

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Combinations of $(0,1)$-Matrices with equal row and colum sum

Published on 27 Nov 2020 - 15:34

score 133 · Answer 14 · 2020-11-27 17:02:47

133

Views

Finite sum of combinations

Published on 27 Nov 2020 - 17:02

score 54 · Answer 15 · 2020-11-30 12:36:36

54

Views

Problem on combinatorics and counting.

Published on 30 Nov 2020 - 12:36

List Question

Proving $\sum_{k=0}^{n}\left(\sum_{l=0}^{k}\binom{n}{k}\binom{k}{l} l\right)=n \times 3^{n-1}$ with a combinatoric argument

infinite sum of inverse binomial coefficient encountered in Bayesian treatment of the German tank problem

How many possible Barcodes are there of width $12$?

Combinatorial Proof of $|T| \leq 2 \binom{n}{\lfloor n/2 \rfloor}$

Combinatoric Proof to show the number of good vectors is at most $\binom{n}{\lfloor n/2 \rfloor}$

Interesting question about exponential generating function of the number of partitions under a certain statistic.

prove the identity $\sum_{k=0}^n {s+k \choose k}{n-k \choose m} = {s+n+1 \choose s+m+1} $

Proving identity through combinatorial model

Find the value of $\frac{\sum_{k<\frac n2} (n-2k){n \choose k}}{2^n-1}$

Number of independent functions for 3 bit strings

Can this be proved using Combinatorics or generating functions?

How would I prove $\sum_{p=1}^{n}\binom{n}{p}p^m(-1)^p=0, m \in \mathbb{N}, 1\leq m < n $ via induction?

Combinations of $(0,1)$-Matrices with equal row and colum sum

Finite sum of combinations

Problem on combinatorics and counting.

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