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Smallest Number $k \in \mathbb{N}$ Such That $(2k-9)! \equiv 0\pmod{k!^2}$

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#number-theory #modular-arithmetic #recreational-mathematics #factorial
2.4k
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Swinging factorial and swinging constant

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#factorial #applications #constants
65
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Determine $I_n=\int_{-\infty}^\infty t^ne^{-\frac{t^2}{a}}dt$

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#calculus #integration #factorial
308
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Series with double factorial

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#sequences-and-series #taylor-expansion #factorial
48
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About $n! > (\frac{n}{e})^n$ in "Introduction to Algorithms 3rd Edition" by CLRS.

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#combinatorics #asymptotics #factorial
178
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For which values of $ x$ we have $\sum\limits_{n=0}^{\infty}x^{\tan(n!)-n!}$ converges?

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#sequences-and-series #trigonometry #factorial
42
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Closed form of $\sum _{i=1}^n\:\frac{\left(m-i\right)!}{\left(n-i\right)!}$

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#summation #factorial
149
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How do I simplify factorials?

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#algebra-precalculus #factorial
130
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Evaluate $\sum_{n=1}^{50}n\cdot n!$.

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#sequences-and-series #summation #factorial
320
Views

Why is gamma function defined such that $\Gamma (n)=(n-1)!$ rather then $\Gamma(n)=n!$

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#factorial #math-history #gamma-function
74
Views

Show that $n^2<n!$ for all $n\geq 4$

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#elementary-number-theory #inequality #induction #factorial
121
Views

Are the Bernoulli numbers $B_{2n}$ given by an elementary function of $n$?

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#factorial #elementary-functions #bernoulli-numbers #bernoulli-polynomials
50
Views

Is there a closed form to this summation?

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#summation #combinations #factorial #closed-form
44
Views

My logic is wrong. Please explain why?

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#combinatorics #permutations #combinations #factorial #permutation-cycles
22
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Show that $\frac{(J-1)!}{2!(J-3)!}= \sum_{h=2}^{J-1}(h-1) $

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#combinatorics #factorial

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