Hey there, I know that

$\displaystyle \frac{t}{e^t-1} = \sum_{k=0}^\infty \frac{B_k}{k!} t^k$, where $\displaystyle B_k$ are the Bernoulli numbers. I am looking for a sequence $\displaystyle a_k$, such that $\displaystyle \frac{t}{e^t+e^{-t}} = \sum_{k=0}^\infty a_k t^k$.

Any ideas?