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

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

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

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