Question

Two identities involving binomial coefficients and double factorials

score 196 · Answer 1 · 2026-02-23 08:23:28

196

Views

Two identities involving binomial coefficients and double factorials

Published on 23 Feb 2026 - 8:23

score 97 · Answer 2 · 2023-05-25 14:59:52

97

Views

Solve for f(x) if f(x)f(-x)=g(x)

Published on 25 May 2023 - 14:59

score 85 · Answer 3 · 2023-05-27 21:32:28

85

Views

Binomial proof of $n! = n^r - n(n - 1)^r + \frac{n(n-1)}{2!}\left(n -2 \right)^r - \dots$ when $r = n$

Published on 27 May 2023 - 21:32

score 125 · Answer 4 · 2026-03-28 14:56:55

125

Views

How long before someone is ahead by 10 in a game of flipping a coin?

Published on 28 Mar 2026 - 14:56

score 126 · Answer 5 · 2026-03-30 15:14:15

126

Views

Why does a sum of factorials behave differently from single factorials?

Published on 30 Mar 2026 - 15:14

score 442 · Answer 6 · 2026-03-30 15:13:26

442

Views

Does using pre-computed squares speed up significantly the calculation of factorial $n!$?

Published on 30 Mar 2026 - 15:13

score 130 · Answer 7 · 2026-03-29 08:20:55

130

Views

A very interesting integral: $\int\limits^{2}_{1}\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}dx$

Published on 29 Mar 2026 - 8:20

score 62 · Answer 8 · 2023-06-06 07:27:48

62

Views

Show that $\sum_{m=1}^nm\cdot m!=(n+1)!-1 \forall n\ge 1$

Published on 06 Jun 2023 - 7:27

score 246 · Answer 9 · 2026-03-28 05:28:42

246

Views

Question about the divisibility of a sum

Published on 28 Mar 2026 - 5:28

score 64 · Answer 10 · 2023-06-09 01:07:31

64

Views

Combinatorics question - Round of 8 draw

Published on 09 Jun 2023 - 1:07

score 92 · Answer 11 · 2026-03-25 22:04:19

92

Views

Integral of $\int^{2\pi}_0 \sin^{2n}(x) \cos^{2m}(x)\ dx$

Published on 25 Mar 2026 - 22:04

score 91 · Answer 12 · 2023-06-12 14:33:20

91

Views

But why does any $\Gamma(z)\Gamma(1-z)\gets\pi\csc(\pi z)$?

Published on 12 Jun 2023 - 14:33

score 132 · Answer 13 · 2023-06-21 12:22:26

132

Views

A number-theoretic proof that $(n^2)!/(n!)^{n+1}$ is an integer

Published on 21 Jun 2023 - 12:22

score 21 · Answer 14 · 2023-06-21 15:32:17

21

Views

Are there infinite triplets that satisfy a! = b!⋅c! where a ≠ b+1?

Published on 21 Jun 2023 - 15:32

score 140 · Answer 15 · 2023-06-23 00:08:49

140

Views

Closed form solution for indexing combinations from n choose r

Published on 23 Jun 2023 - 0:08

List Question

Two identities involving binomial coefficients and double factorials

Solve for f(x) if f(x)f(-x)=g(x)

Binomial proof of $n! = n^r - n(n - 1)^r + \frac{n(n-1)}{2!}\left(n -2 \right)^r - \dots$ when $r = n$

How long before someone is ahead by 10 in a game of flipping a coin?

Why does a sum of factorials behave differently from single factorials?

Does using pre-computed squares speed up significantly the calculation of factorial $n!$?

A very interesting integral: $\int\limits^{2}_{1}\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}dx$

Show that $\sum_{m=1}^nm\cdot m!=(n+1)!-1 \forall n\ge 1$

Question about the divisibility of a sum

Combinatorics question - Round of 8 draw

Integral of $\int^{2\pi}_0 \sin^{2n}(x) \cos^{2m}(x)\ dx$

But why does any $\Gamma(z)\Gamma(1-z)\gets\pi\csc(\pi z)$?

A number-theoretic proof that $(n^2)!/(n!)^{n+1}$ is an integer

Are there infinite triplets that satisfy a! = b!⋅c! where a ≠ b+1?

Closed form solution for indexing combinations from n choose r

Trending Questions

Popular # Hahtags

Popular Questions