Question

On compact expressions for determinants of matrices having polynomial entries with binomial coefficients

score 108 · Answer 1 · 2026-04-04 07:52:29

108

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On compact expressions for determinants of matrices having polynomial entries with binomial coefficients

Published on 04 Apr 2026 - 7:52

score 87 · Answer 2 · 2026-03-28 06:40:44

87

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A question on $\int \prod_{j=1}^u \frac{x+j}{j-x}~dx.$

Published on 28 Mar 2026 - 6:40

score 138 · Answer 3 · 2026-03-29 21:19:46

138

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In how many ways can we place $k$ distinct objects into $n$ identical boxes if each box contains atmost one object

Published on 29 Mar 2026 - 21:19

score 524 · Answer 4 · 2026-03-30 06:50:13

524

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How to show $\int_{\mathbb{R}}{t \choose x}^2{x \choose t}~dx = 1$

Published on 30 Mar 2026 - 6:50

score 43 · Answer 5 · 2020-02-03 21:15:18

43

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How to simplify the following combination sum?

Published on 03 Feb 2020 - 21:15

score 63 · Answer 6 · 2026-04-01 12:49:37

63

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Closed form for $\sum_{k=a}^b{n \choose k}{k \choose r}$

Published on 01 Apr 2026 - 12:49

score 365 · Answer 7 · 2020-02-05 09:35:31

365

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Asymptotically $\binom{2n}{n}\approx\frac{2^{2n}}{\sqrt{\pi n}}$ or $\binom{2n}{n}\approx2^{2n}$?

Published on 05 Feb 2020 - 9:35

score 48 · Answer 8 · 2020-02-05 10:21:10

48

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Simplify binomial expression

Published on 05 Feb 2020 - 10:21

score 92 · Answer 9 · 2026-03-25 11:06:46

92

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In the multinomial expansion of $(a+b+c)^5$ , why does "a" have $5 \choose 1$ positions?

Published on 25 Mar 2026 - 11:06

score 134 · Answer 10 · 2020-02-05 14:57:59

134

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$\displaystyle\sum_{k\geq 0}^{} \binom{n}{2k} = \sum_{k \geq 0}^{} \binom{n}{2k+1}$

Published on 05 Feb 2020 - 14:57

score 129 · Answer 11 · 2020-02-06 17:39:36

129

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Is the binomial coefficient linear?

Published on 06 Feb 2020 - 17:39

score 142 · Answer 12 · 2026-03-30 06:46:41

142

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Evaluating the sum $\sum_{k=1}^n \frac{k!}{(k+a)!}$ for a parameter $a$

Published on 30 Mar 2026 - 6:46

score 55 · Answer 13 · 2020-02-08 20:01:48

55

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Help with proving this combinatorial identity?

Published on 08 Feb 2020 - 20:01

score 66 · Answer 14 · 2020-02-09 22:45:32

66

Views

Find my mistake: Prove $\sum_{i=0}^{r} \sum_{j=0}^{c} \binom{i+j}{j}=\binom{r+c+2}{c+1}-1$

Published on 09 Feb 2020 - 22:45

score 92 · Answer 15 · 2020-02-10 04:01:26

92

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simplifying summations inspired by binomial coefficient and binomial distribution

Published on 10 Feb 2020 - 4:01

List Question

On compact expressions for determinants of matrices having polynomial entries with binomial coefficients

A question on $\int \prod_{j=1}^u \frac{x+j}{j-x}~dx.$

In how many ways can we place $k$ distinct objects into $n$ identical boxes if each box contains atmost one object

How to show $\int_{\mathbb{R}}{t \choose x}^2{x \choose t}~dx = 1$

How to simplify the following combination sum?

Closed form for $\sum_{k=a}^b{n \choose k}{k \choose r}$

Asymptotically $\binom{2n}{n}\approx\frac{2^{2n}}{\sqrt{\pi n}}$ or $\binom{2n}{n}\approx2^{2n}$?

Simplify binomial expression

In the multinomial expansion of $(a+b+c)^5$ , why does "a" have $5 \choose 1$ positions?

$\displaystyle\sum_{k\geq 0}^{} \binom{n}{2k} = \sum_{k \geq 0}^{} \binom{n}{2k+1}$

Is the binomial coefficient linear?

Evaluating the sum $\sum_{k=1}^n \frac{k!}{(k+a)!}$ for a parameter $a$

Help with proving this combinatorial identity?

Find my mistake: Prove $\sum_{i=0}^{r} \sum_{j=0}^{c} \binom{i+j}{j}=\binom{r+c+2}{c+1}-1$

simplifying summations inspired by binomial coefficient and binomial distribution

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