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Factorial and Multiplication

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#binomial-coefficients #factorial
156
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Proof that expression is integer, $\frac{(2n)!}{n!(n+1)!}$

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#elementary-number-theory #induction #divisibility #factorial
203
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Problem with injective functions on an explanation of the Birthday problem

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#probability #functions #factorial
105
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$n-\frac{n(n^2-1)}{2!}+\frac{n(n^2-1)(n^2-4)}{2!3!}-\frac{n(n^2-1)(n^2-4)(n^2-9)}{3!4!}+.....$

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#sequences-and-series #number-theory #factorial
91
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Simplify $\frac{a!}{(a+b)!}$

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#algebra-precalculus #factorial
73
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Proving $\int_{-1}^{1}(1-x^2)^n\,\mathrm dx=\frac{2^{2n+1}(n!)^2}{(2n+1)!}$ for $n=0,1,2,3...$

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#calculus #definite-integrals #factorial
107
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Counting number of balanced two-way partition of the set

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#combinatorics #factorial #set-partition
101
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Is there a factorial of the form $p m^2$ greater than 720?

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#number-theory #prime-numbers #factorial #square-numbers
425
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The digital root of factorials from 6! to infinity! is always 9.

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#induction #factorial
808
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What is $2!!!!!!!!!!!!!!!!!!!!$................. (up to?

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#factorial #infinity
124
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Does the equality $ \dfrac{10!}{6!} = 7! $ hold any special (geometric) meaning?

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#combinatorics #intuition #factorial #visualization
795
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$n!$ as product of consecutive numbers

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#factorial
294
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What is the significance of $0!=1$?

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#factorial
1k
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Finding value of unknown in factorial equation

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#permutations #combinations #factorial
148
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Limits and factorials

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#calculus #limits #factorial

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