Derangement death.

$\displaystyle \frac {1}{4! \ .4! \ .2!} \int_0 ^{\infty} e^{-x} (x - 1) (x^2 - 4x + 2)(x^4 - 16x^3 + 72x^2 - 96x + 24)^2 dx = 648$

This function gives the number of the required derangements.