Finding Summation of n^p with Bernoulli Numbers

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Hey everyone,
I need some help trying to figure out how to find the summation of

n
[tex]\sum_{}^{\6}i^p[/tex]
i=0

I was looking on the web and found on Wikipedia this formula off the http://en.wikipedia.org/wiki/Summation" page. It looks like this assuming I copied it right (ignore the periods)

.n......p
[tex]\sum_{}^{\6}i^p = \frac{(n+1)^{p+1}}{p+1} + \sum_{}^{\5} \frac {B_k}{p-k+1} \left(\begin{array}{cc}p\\k\end{array}\right)(n+1)^{p-k+1}[/tex]
i=0......k=1

I know how to do the math and know what almost all the variables mean. The only one that gets in my way of using this formula is [tex]B_k[/tex]. Now [tex]B_k[/tex], as wikipedia says stands for kth Bernoulli number. I've tried looking at Google and Wikipedia to find out what the Bernoulli number is but I can't seem to find out what it really is. Can someone explain to me what the Bernoulli number is and how to calculate or find it? I don't know how to.

Many Thanks

 

[CRGreathouse]

Rather than calculate them, you could look them up on a table, like:
http://en.wikipedia.org/wiki/Bernoulli_number#Values_of_the_Bernoulli_numbers