Question

Is there an expression for the coefficients of the falling factorial $x^{\underline n} \equiv x (x-1) \dots (x-n+1)$?

score 437 · Answer 1 · 2026-03-27 02:36:09

437

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Is there an expression for the coefficients of the falling factorial $x^{\underline n} \equiv x (x-1) \dots (x-n+1)$?

Published on 27 Mar 2026 - 2:36

score 35 · Answer 2 · 2020-04-18 00:29:33

35

Views

Equations Involving Factorial

Published on 18 Apr 2020 - 0:29

score 31 · Answer 3 · 2020-04-18 10:44:11

31

Views

Is there known integer polynomial $f(p,q)$ for which $(p-q)!=p!-q!+f(p,q)$?

Published on 18 Apr 2020 - 10:44

score 105 · Answer 4 · 2026-03-27 03:43:06

105

Views

I Need help creating an intuitive answer to the sum of $1(1!) + 2(2!) + 3(3!) +\cdots+ n(n!)$

Published on 27 Mar 2026 - 3:43

score 244 · Answer 5 · 2020-04-22 23:00:23

244

Views

How many solutions for this equation using combinatorics?

Published on 22 Apr 2020 - 23:00

score 253 · Answer 6 · 2020-04-24 02:41:59

253

Views

Proving interesting identity with partial sums of Pascal's triangle rows

Published on 24 Apr 2020 - 2:41

score 109 · Answer 7 · 2020-04-26 13:02:39

109

Views

How to prove that an equation with two variables does have a set of integer solutions.

Published on 26 Apr 2020 - 13:02

score 77 · Answer 8 · 2020-04-26 14:55:00

77

Views

proof $k!j!\leq(j+k)!$ by induction

Published on 26 Apr 2020 - 14:55

score 380 · Answer 9 · 2020-05-02 13:02:57

380

Views

Reference request - identity in central factorial numbers

Published on 02 May 2020 - 13:02

score 71 · Answer 10 · 2020-05-04 14:23:14

71

Views

Need help in deducing an inequality related to factorial which is to be used in number theory

Published on 04 May 2020 - 14:23

score 109 · Answer 11 · 2020-05-05 04:09:55

109

Views

Evaluating $\lim_\limits{x\to 3}\left(\frac{\left(x!-2x\right)}{x-3}\right)$

Published on 05 May 2020 - 4:09

score 234 · Answer 12 · 2020-05-06 11:12:14

234

Views

Can we write $n!$ as $n^n$

Published on 06 May 2020 - 11:12

score 71 · Answer 13 · 2020-05-08 05:36:42

71

Views

Comparing a binomial coefficient to a fraction of factorials

Published on 08 May 2020 - 5:36

score 24 · Answer 14 · 2020-05-08 09:39:48

24

Views

How many combinations can be generated with this set?

Published on 08 May 2020 - 9:39

score 70 · Answer 15 · 2020-05-09 12:28:38

70

Views

Identity $\frac { ( rn+j+1)! } { ( j+1)! {(j! × ( n-j)!)}^r}\leq { (2r+1) }^{ rn+j+1} $

Published on 09 May 2020 - 12:28

List Question

Is there an expression for the coefficients of the falling factorial $x^{\underline n} \equiv x (x-1) \dots (x-n+1)$?

Equations Involving Factorial

Is there known integer polynomial $f(p,q)$ for which $(p-q)!=p!-q!+f(p,q)$?

I Need help creating an intuitive answer to the sum of $1(1!) + 2(2!) + 3(3!) +\cdots+ n(n!)$

How many solutions for this equation using combinatorics?

Proving interesting identity with partial sums of Pascal's triangle rows

How to prove that an equation with two variables does have a set of integer solutions.

proof $k!j!\leq(j+k)!$ by induction

Reference request - identity in central factorial numbers

Need help in deducing an inequality related to factorial which is to be used in number theory

Evaluating $\lim_\limits{x\to 3}\left(\frac{\left(x!-2x\right)}{x-3}\right)$

Can we write $n!$ as $n^n$

Comparing a binomial coefficient to a fraction of factorials

How many combinations can be generated with this set?

Identity $\frac { ( rn+j+1)! } { ( j+1)! {(j! × ( n-j)!)}^r}\leq { (2r+1) }^{ rn+j+1} $

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