These are Bell numbers, <a href="http://oeis.org/search?q=1%2C1%2C2%2C5%2C15%2C52&language=english&go=Search">A000110</a>. The relatively explicit formula given in the Encyclopedia: $$a_n=\frac{2n!}{\pi e}\Im\left(\int_{0}^{\pi} e^{e^{e^{ix}}} \sin(nx) dx \right)$$