Here http://arxiv.org/pdf/0811.4488v1 in Theorem 1 while prooving uniform convergence of
$\sum_{k=0}^{\infty}\lambda^k{\widetilde{X}}^{(2k)}$
it's said that
$|{\widetilde{X}}^{(2k)}| \leq (\max|ru_0^2|)^k \cdot (\max|\frac{1}{pu_0^2}|)^k \cdot \frac{|b-a|^{2k}}{(2k)!}$
Where did they get factor $\frac{1}{(2k)!}$?