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Identity involving double sum with factorials

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#summation #binomial-coefficients #factorial #pochhammer-symbol
67
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Evaluating $\sum_{i=0}^{H-1} \dfrac{(-1)^i}{i! (H-1-i)! (k+i)}$

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#calculus #combinatorics #factorial #gamma-function
76
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Solve $(n+1)^k-1=n!$

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#number-theory #diophantine-equations #factorial #binomial-theorem
144
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How many ways are there to choose an arbitrary number of students (including the possibility of choosing 0 students) from 6 students?

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#combinatorics #factorial
45
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$ \sum_{x=1}^n {{n-1} \choose {x-1}} {N \choose x} = {{N+n-1}\choose n}$

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#combinatorics #combinations #factorial
87
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Is $\frac{y!}{y+1}$ an integer if $y$ is an odd number?

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#elementary-number-theory #factorial
178
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Can $n!$ be expressed as the sum of $n$ powers of 2?

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#elementary-number-theory #factorial
70
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Is this function increasing in $x$?

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#calculus #factorial #monotone-functions
66
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Prove that an equation with two integer variables has no solution

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#combinatorics #factorial
66
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Prove that $\sum_{q=0}^{d-r}\sum_{s=r+q}^{d}{{\binom {r-1+q}{r-1}}(r-1)!s}=\sum_{s=r}^{d}{\binom{s}{r}(r-1)!s}$ by sum manipulation

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#combinatorics #summation #binomial-coefficients #factorial
44
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'Provide the answer as a function of N. You are not required to show the derivation process.' What should the answer be?

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#functions #algorithms #factorial
146
Views

What is $(3n+3)!$ equal to

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#factorial
285
Views

Primes made from alternating factorials

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#elementary-number-theory #recreational-mathematics #factorial
518
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Inequality $(n!)^3<n^n(n+1/2)^{2n}$

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#inequality #factorial
146
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Find all possible values of a natural number $n$ such that $a! + b! = 5^n$

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#elementary-number-theory #factorial

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