Riemann Zeta function of even numbers

[dimension10]

Given that

[tex]\zeta (2n)=\frac{{\pi}^{2n}}{m}[/tex]

Then how do you find m with respect to n where n is a natural number.

For

n=1, m=6
n=2, m=90
n=3, m=945
n=4, m=9450
n=5, m=93555
n=6, m=[tex]\frac{638512875}{691}[/tex]
n=7, m=[tex]\frac{18243225}{2}[/tex]
n=8, m=[tex]\frac{325641566250}{3617}[/tex]
n=9, m=[tex]\frac{38979295480125}{43867}[/tex]
n=10, m=[tex]\frac{1531329465290625}{174611}[/tex]

But I don't see any pattern.

Thanks.

 

[Hurkyl]

I would find it by consulting wikipedia.

 

[dimension10]

Thanks.