Mister Exam
Expression simplification/
Least common denominator/
factorial(n/2*(n-1))/(factorial(n-1)*factorial((n-1)*(n-2)/2))
Least common denominator factorial(n/2*(n-1))/(factorial(n-1)*factorial((n-1)*(n-2)/2))
The solution
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[src]
/n \
|-*(n - 1)|!
\2 /
---------------------------
/(n - 1)*(n - 2)\
(n - 1)!*|---------------|!
\ 2 /
$$\frac{\left(\frac{n}{2} \left(n - 1\right)\right)!}{\left(\frac{\left(n - 2\right) \left(n - 1\right)}{2}\right)! \left(n - 1\right)!}$$
factorial((n/2)*(n - 1))/((factorial(n - 1)*factorial(((n - 1)*(n - 2))/2)))
General simplification
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/ 2 \
| n n|
2*Gamma|1 + -- - -|
\ 2 2/
----------------------------------------------
/ 2 \
| n 3*n|
(-1 + n)*(-2 + n)*Gamma(n)*Gamma|1 + -- - ---|
\ 2 2 /
$$\frac{2 \Gamma\left(\frac{n^{2}}{2} - \frac{n}{2} + 1\right)}{\left(n - 2\right) \left(n - 1\right) \Gamma\left(n\right) \Gamma\left(\frac{n^{2}}{2} - \frac{3 n}{2} + 1\right)}$$
2*gamma(1 + n^2/2 - n/2)/((-1 + n)*(-2 + n)*gamma(n)*gamma(1 + n^2/2 - 3*n/2))
Trigonometric part
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/n*(-1 + n)\
|----------|!
\ 2 /
------------------------------
/(-1 + n)*(-2 + n)\
|-----------------|!*(-1 + n)!
\ 2 /
$$\frac{\left(\frac{n \left(n - 1\right)}{2}\right)!}{\left(\frac{\left(n - 2\right) \left(n - 1\right)}{2}\right)! \left(n - 1\right)!}$$
factorial(n*(-1 + n)/2)/(factorial((-1 + n)*(-2 + n)/2)*factorial(-1 + n))
Combining rational expressions
[src]
/n*(-1 + n)\
|----------|!
\ 2 /
------------------------------
/(-1 + n)*(-2 + n)\
|-----------------|!*(-1 + n)!
\ 2 /
$$\frac{\left(\frac{n \left(n - 1\right)}{2}\right)!}{\left(\frac{\left(n - 2\right) \left(n - 1\right)}{2}\right)! \left(n - 1\right)!}$$
factorial(n*(-1 + n)/2)/(factorial((-1 + n)*(-2 + n)/2)*factorial(-1 + n))
Powers
[src]
/n*(-1 + n)\
|----------|!
\ 2 /
------------------------------
/(-1 + n)*(-2 + n)\
|-----------------|!*(-1 + n)!
\ 2 /
$$\frac{\left(\frac{n \left(n - 1\right)}{2}\right)!}{\left(\frac{\left(n - 2\right) \left(n - 1\right)}{2}\right)! \left(n - 1\right)!}$$
factorial(n*(-1 + n)/2)/(factorial((-1 + n)*(-2 + n)/2)*factorial(-1 + n))
Numerical answer
[src]
factorial((n/2)*(n - 1))/(factorial(((n - 1)*(n - 2))/2)*factorial(n - 1))
factorial((n/2)*(n - 1))/(factorial(((n - 1)*(n - 2))/2)*factorial(n - 1))
Combinatorics
[src]
/ 2 \
| n n|
2*Gamma|1 + -- - -|
\ 2 2/
----------------------------------------------
/ 2 \
| n 3*n|
(-1 + n)*(-2 + n)*Gamma(n)*Gamma|1 + -- - ---|
\ 2 2 /
$$\frac{2 \Gamma\left(\frac{n^{2}}{2} - \frac{n}{2} + 1\right)}{\left(n - 2\right) \left(n - 1\right) \Gamma\left(n\right) \Gamma\left(\frac{n^{2}}{2} - \frac{3 n}{2} + 1\right)}$$
2*gamma(1 + n^2/2 - n/2)/((-1 + n)*(-2 + n)*gamma(n)*gamma(1 + n^2/2 - 3*n/2))
Rational denominator
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/ 2 \
|n n|
|-- - -|!
\2 2/
------------------------------
/(-1 + n)*(-2 + n)\
|-----------------|!*(-1 + n)!
\ 2 /
$$\frac{\left(\frac{n^{2}}{2} - \frac{n}{2}\right)!}{\left(\frac{\left(n - 2\right) \left(n - 1\right)}{2}\right)! \left(n - 1\right)!}$$
factorial(n^2/2 - n/2)/(factorial((-1 + n)*(-2 + n)/2)*factorial(-1 + n))
Common denominator
[src]
/ 2 \
|n n|
|-- - -|!
\2 2/
-------------------------
/ 2 \
| n 3*n|
(-1 + n)!*|1 + -- - ---|!
\ 2 2 /
$$\frac{\left(\frac{n^{2}}{2} - \frac{n}{2}\right)!}{\left(n - 1\right)! \left(\frac{n^{2}}{2} - \frac{3 n}{2} + 1\right)!}$$
factorial(n^2/2 - n/2)/(factorial(-1 + n)*factorial(1 + n^2/2 - 3*n/2))