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Alternate method for finding ways of distribution

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#combinatorics #permutations #factorial
193
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First digit of a factorial without calculating it

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#factorial
260
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Proof that each prime power of ${2n \choose n}$ is $\leq \log_p 2n$

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#binomial-coefficients #factorial #prime-factorization
242
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Recurrence relations of the form $T(n) = n T(n-1) + ...$

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#asymptotics #recurrence-relations #factorial
121
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How to prove $\lim_{n\to \infty} \frac{n!}{n^n}$ is zero?

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#limits #analysis #factorial
62
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Existence of super Wilson numbers

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#number-theory #prime-numbers #factorial
150
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prove $\prod_{i=0}^{n}x-\frac{i}{n}\le\frac{n!}{4n^{n+1}}$ for any $x\in[0,1]$ and $n>2$

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#inequality #polynomials #factorial #numerical-calculus
55
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Prove that $\sum_{i=0}^{\infty}(-1)^{3n} \dfrac{x^{4n}}{(5n)!}$ converges absolutely

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#convergence-divergence #factorial
106
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How many entries in a bisymmetric matrix can be chosen independently?

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#linear-algebra #matrices #permutations #factorial #symmetric-matrices
61
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What is the term used for a "factorial" of prime numbers ? Is there such a definition?

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#prime-numbers #terminology #definition #factorial
372
Views

A curious infinite product of factorials

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#analysis #factorial #gamma-function #infinite-product #conjectures
194
Views

Why are we having factorial sign when there is already the $\Pi$ notation in use?

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#notation #factorial #products
100
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What is the last non-zero digit of $((\dots(((1!)!+2!)!+3!)!+\dots)!+1992!)!$?

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#number-theory #elementary-number-theory #factorial #integers #decimal-expansion
351
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Simplifying to a expression with a double factorial

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#factorial #gamma-function #beta-function
65
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How to solve multiple inequalities?

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#inequality #factorial

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