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Can $\{n!\log n\}$ converge to $1$?

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#real-analysis #number-theory #limits #factorial #fractional-part
46
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Prove this factorial fractional equivalence

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#combinatorics #analysis #factorial #divisor-sum
135
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What is known about this specialization of the falling factorial involving primes?

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#prime-numbers #factorial #products
332
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What is a factorial prior?

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#probability #probability-theory #factorial #information-theory #bayesian
129
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Can we provide a good estimation for $(n!)!$?

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#approximation #factorial #approximation-theory #stirling-numbers
84
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Is there any way to simplify sum $\frac{1}{ (n - 2m)! m!}$?

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#factorial
115
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Closed form if any for infinite product

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#factorial #infinite-product
7.8k
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Find the number of consecutive zeros at the end of the following numbers $100!+200!$

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#number-theory #elementary-number-theory #numerical-methods #factorial
241
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Can't prove this algebraically $\sum\limits_{i = 0}^n { n \choose i } \, !i = n! $

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#combinatorics #permutations #binomial-coefficients #factorial #derangements
153
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Is it true that $\sum_{S \subset N \setminus \{i\}} {|S|!(n-|S|-1)!}=n!$, where $N=\{1, 2, \dots, n\}$ and $i \in N$?

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#combinatorics #summation #factorial #game-theory
60
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Factorials with arbitrary numbers enquiry?

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#factorial
57
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Help on induction, couldn't make both side the same value

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#discrete-mathematics #induction #factorial #recursion
152
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Fraction of $1$s in binary representation of $n!$

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#number-theory #limits #factorial #limsup-and-liminf #binary
70
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why $\ln(n!)=n\ln(n)-n+\frac{1}{2}\ln(2\pi n)+o(1)$?

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#asymptotics #factorial
127
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Calculate $\lim_{n \rightarrow \infty}$ ($n!e-[n!e]$)?

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#limits #factorial #ceiling-and-floor-functions

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