> The Bernoulli numbers are related to  the exponential form of the
> characteristic series of the Witten genus.

And



> Bernoulli numbers are related to the order of some groups in the image of
> the J-homomorphism

Bernoulli numbers are especial case of Poly-Bernoulli numbers which are very important in combinatorics.

In definition of Poly-Bernoulli numbers
 
$${Li_{k}(1-e^{-x}) \over 1-e^{-x}}=\sum_{n=0}^{\infty}B_{n}^{(k)}{x^{n}\over n!}$$

he used of poly-logarithm which has some relationships with poly-gamma , where The $B_{n}^{(1)}$ are the usual Bernoulli numbers. 

A combinatorial interpretation is that the poly-Bernoulli numbers of negative index enumerate the set of n by k (0,1)-matrices uniquely reconstructible from their row and column sums.

Here you can find [combinatorics of Poly-Bernoulli numbers][1] 

For $\zeta(2n+1)$ Poly-Bernoulli numbers are more functional , see [here][2]


  [1]: http://vvi.ejf.hu/wp-content/uploads/2013/08/PB_okt_07.pdf
  [2]: http://www.springer.com/us/book/9784431549185