gives the number of permutations of n objects that leave no object fixed.


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For non-integer n, the numerical value of Subfactorial[n] is given by Gamma[n+1,-1]/E.
  • Subfactorial can be evaluated to arbitrary numerical precision.
  • A permutation in which no object appears in its natural place is called a derangement.
  • Subfactorial automatically threads over lists.
  • Subfactorial[0] gives 1.
Introduced in 2007