Power series of $\tan(z)$ In the power series of 

$$\tan(z)=\sum_{k=0}^{\infty }B_{2k}\frac{(-4)^k(1-4^k)x^{2k-1}}{(2k!)},$$ what is $B_{2k}$? 

What's the mathematical expression of it?
Thanks in advance.

$B_{2k}$ are Bernoulli numbers.  As they have numerous properties, a full treatment would be too lengthy to include as an answer, so I will refer you to here:  http://en.wikipedia.org/wiki/Bernoulli_number
