Abstract
We give a short generating function proof of the Almkvist-Meurman theorem: For integers \(h\) and \(k\ne0\), define the numbers \(M_n(h,k)\) by \(kx(e^{hx}-1)/(e^{kx}-1)=\sum_{n=0}^\infty M_n(h,k) x^n/n!\). Equivalently, \(M_n(h,k) = k^n(B_n(h/k) - B_n)\), where \(B_n(u)\) is the Bernoulli polynomial. Then \(M_n(h,k)\) is an integer. The proof is related to Postnikov's functional equation for the generating function for intransitive trees.