# Coefficients in Hirzebruch polynomial and divisibility of Bernoulli numbers: reference request

I seek a reference for the fact that "coefficients of the Hirzebruch $L$-polynomial have odd denominators". The coefficients are $$\frac{2^{2k}(2^{2k-1}-1)B_k}{(2k)!}$$ where $B_k$ is the Bernoulli number, but I cannot locate the appropriate divisibility property of $B_k$. Of course, $2^{2k-1}-1$ is odd, so it can be ignored.

-

Thank you. One needs also a little combinatorial argument on how many powers of two are in $(2k)!$, but I think I got it. –  Igor Belegradek Jun 4 '12 at 23:24