It seems that the $n$th cumulant of the uniform distribution on the interval $[-1,0]$ is $B_n/n$, where $B_n$ is the $n$th Bernoulli number.
And also $-\zeta(1-n) = B_n/n$, where $\zeta$ is Riemann's $\zeta$ function.
Is there some reason why one should expect these to be the same, as opposed to proofs that convince you that they are?