List questions from factorial

Published on 28 Jan 2017 - 12:33

466

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How to show that $\sum_{k} (-1)^k{{a+b}\choose{a+k}}{{b+c}\choose{b+k}}{{c+a}\choose{c+k}} = \frac{(a+b+c)!}{a!b!c!}$

Published on 26 Mar 2026 - 6:31

29

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Find the solution to each of distinct positive x_i 's

Published on 30 Jan 2017 - 4:56

546

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Relative error in Stirling series

Published on 30 Jan 2017 - 23:14

5.4k

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Find all positive integers a,b,c to the equation a!b!= a!+b!+c!

Published on 31 Jan 2017 - 20:37

274

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How to prove that the determinant of this matrix is n! (by induction)

Published on 01 Feb 2017 - 0:01

242

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Sum of Hermite functions with factorials

Published on 25 Mar 2026 - 6:34

980

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A Diophantine equation involving factorial

Published on 02 Feb 2017 - 11:50

471

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Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$

Published on 02 Feb 2017 - 22:52

126

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Remainder of $\sum_{x=1}^{312} x \times x!$ divided by 2016

Published on 28 Mar 2026 - 3:27

1.2k

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How to show that $(n-k)!n^{\underline{k}}=\Gamma(n+1)$

Published on 05 Feb 2017 - 14:35

8.2k

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Prove Big-Oh using Induction

Published on 06 Feb 2017 - 0:33

356

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Squarefree part of $n!$

Published on 06 Feb 2017 - 0:34

141

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When is $m! > \binom{n}{m}$?

Published on 10 Feb 2017 - 18:20

104

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Exact Value for an Infinite Series

Published on 11 Feb 2017 - 23:58

List Question

A discrete summation in probability theory

How to show that $\sum_{k} (-1)^k{{a+b}\choose{a+k}}{{b+c}\choose{b+k}}{{c+a}\choose{c+k}} = \frac{(a+b+c)!}{a!b!c!}$

Find the solution to each of distinct positive x_i 's

Relative error in Stirling series

Find all positive integers a,b,c to the equation a!b!= a!+b!+c!

How to prove that the determinant of this matrix is n! (by induction)

Sum of Hermite functions with factorials

A Diophantine equation involving factorial

Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$

Remainder of $\sum_{x=1}^{312} x \times x!$ divided by 2016

How to show that $(n-k)!n^{\underline{k}}=\Gamma(n+1)$

Prove Big-Oh using Induction

Squarefree part of $n!$

When is $m! > \binom{n}{m}$?

Exact Value for an Infinite Series

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