Question

Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.

score 232 · Answer 1 · 2018-11-04 23:24:45

232

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Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.

Published on 04 Nov 2018 - 23:24

score 82 · Answer 2 · 2018-11-05 00:32:29

82

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Roads in a grid $(s+m+1) \times (n-m)$

Published on 05 Nov 2018 - 0:32

score 452 · Answer 3 · 2018-11-05 06:54:48

452

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How to construct a block-walking argument proof for $\sum_{k=0}^l {l-k \choose m} {q+k \choose n} = {l+q+1 \choose m+n+1}$?

Published on 05 Nov 2018 - 6:54

score 50 · Answer 4 · 2018-11-05 07:05:02

50

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Evaluate a series with binomial coefficients

Published on 05 Nov 2018 - 7:05

score 103 · Answer 5 · 2026-03-27 01:47:38

103

Views

How to find the sum of the given series: $\sum_{k=0}^{\min(n ,m)} \binom{n}{k} \binom{m}{k}$?

Published on 27 Mar 2026 - 1:47

score 165 · Answer 6 · 2026-03-27 01:47:39

165

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How can I find the number of dissimilar or distinct terms in $(1+x + x^2 +x^3)^n$?

Published on 27 Mar 2026 - 1:47

score 134 · Answer 7 · 2018-11-07 06:38:12

134

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How to prove $\sum_{k=0}^{n-j}(-1)^k{n-j\choose k}{n+j+k\choose 2j+1+k}$ equal to zero?

Published on 07 Nov 2018 - 6:38

score 55 · Answer 8 · 2018-11-07 11:13:08

55

Views

Proving $|Z| \leq \binom{n}{l}/ \binom{m}{l}$

Published on 07 Nov 2018 - 11:13

score 134 · Answer 9 · 2026-03-27 18:34:55

134

Views

Finding generating function for $ h_{n} = h_{n-1} + \binom{n+1}{3} + n$

Published on 27 Mar 2026 - 18:34

score 145 · Answer 10 · 2018-11-09 05:28:03

145

Views

Nested sum of binomial coefficient in closed form

Published on 09 Nov 2018 - 5:28

score 76 · Answer 11 · 2018-11-09 16:54:01

76

Views

Would it be reasonable to define $\binom{n}{n+1} = 0$?

Published on 09 Nov 2018 - 16:54

score 312 · Answer 12 · 2026-03-25 22:26:52

312

Views

Recurrence Relations-For n∈\N0 let w(n) denote the number of 1s in the binary representation of n. For example, w(9) = 2

Published on 25 Mar 2026 - 22:26

score 188 · Answer 13 · 2026-03-27 16:47:21

188

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Constrained combinatorial question: 2 types of balls divided into k groups with limits

Published on 27 Mar 2026 - 16:47

score 57 · Answer 14 · 2018-11-11 09:50:50

57

Views

Binomial inequality : $\binom{n}{k} \leq n^k$

Published on 11 Nov 2018 - 9:50

score 38 · Answer 15 · 2018-11-11 13:28:19

38

Views

Solving for $n$

Published on 11 Nov 2018 - 13:28

List Question

Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.

Roads in a grid $(s+m+1) \times (n-m)$

How to construct a block-walking argument proof for $\sum_{k=0}^l {l-k \choose m} {q+k \choose n} = {l+q+1 \choose m+n+1}$?

Evaluate a series with binomial coefficients

How to find the sum of the given series: $\sum_{k=0}^{\min(n ,m)} \binom{n}{k} \binom{m}{k}$?

How can I find the number of dissimilar or distinct terms in $(1+x + x^2 +x^3)^n$?

How to prove $\sum_{k=0}^{n-j}(-1)^k{n-j\choose k}{n+j+k\choose 2j+1+k}$ equal to zero?

Proving $|Z| \leq \binom{n}{l}/ \binom{m}{l}$

Finding generating function for $ h_{n} = h_{n-1} + \binom{n+1}{3} + n$

Nested sum of binomial coefficient in closed form

Would it be reasonable to define $\binom{n}{n+1} = 0$?

Recurrence Relations-For n∈\N0 let w(n) denote the number of 1s in the binary representation of n. For example, w(9) = 2

Constrained combinatorial question: 2 types of balls divided into k groups with limits

Binomial inequality : $\binom{n}{k} \leq n^k$

Solving for $n$

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