New posts in factorial

Prove $\sum_{q=\alpha}^p \binom{q}{\alpha} \binom{p}{q}\frac{(-1)^q(-q)^p}{q^\alpha}=\frac{p!}{\alpha!}.$

summation binomial-coefficients factorial

On the Limit of Stirling's Approximation

number-theory reference-request asymptotics factorial

Is $\ 7!=5040\ $ the largest highly composite factorial?

number-theory factorial divisor-counting-function

Prove that $\frac{(3 a+3 b) !(2 a) !(3 b) !(2 b) !}{(2 a+3 b) !(a+2 b) !(a+b) ! a !(b !)^{2}}$ is an integer.

elementary-number-theory inequality contest-math factorial ceiling-and-floor-functions

OverflowError: long int too large to convert to float in python

python overflow factorial

Is there a closed-form equation for $n!$? If not, why not?

combinatorics algorithms factorial closed-form

Prove that $n! \geq 2^{n-1}$ for $ n\geq1$ [duplicate]

inequality induction factorial

Find $\lim_{n \to +\infty} \frac{1}{n}\sqrt[n]{\frac{(2n)!}{n!}} $ using Riemann integral [duplicate]

calculus real-analysis limits factorial radicals

Solve by induction: $n!>(n/e)^n$

inequality induction factorial

Why $0!$ is equal to $1$? [duplicate]

combinatorics factorial

Prove by induction that $n! > n^2$ [duplicate]

inequality induction factorial

Proof that $\lim\limits_{h \to \infty} \frac{h!}{h^k(h-k)!}=1 $ for any $ k $ [duplicate]

limits factorial

Proof for convergence of a given progression $a_n := n^n / n!$

sequences-and-series limits convergence-divergence factorial

Convergence of $a_n= \frac{n!}{n^n}$? [duplicate]

calculus sequences-and-series limits exponentiation factorial

Example of O(n!)?

java algorithm big-o complexity-theory factorial

Factorial of 0 - a convenience? [duplicate]

permutations factorial

Ways to find $\frac{1}{2\cdot4}+\frac{1\cdot3}{2\cdot4\cdot6}+\frac{1\cdot3\cdot5}{2\cdot4\cdot6\cdot8}+\cdots$

sequences-and-series factorial binomial-theorem

Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$ [duplicate]

proof-writing induction divisibility factorial

$a!b!$ multiple of $a! + b!$ implies $3a\geq 2b + 2$

number-theory inequality contest-math divisibility factorial

Why $ \lim_{n\rightarrow \infty} \frac{n!}{n^{k}(n-k)! } =1 $?

limits factorial