Power series of $\tan(z)$

Question

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.

Answer 1

$B_{2k}$ 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