Subfactorial

Subfactorial[n]

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

Details

  • 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.

Examples

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Basic Examples  (1)

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Scope  (6)

Applications  (1)

Properties & Relations  (5)

Neat Examples  (1)

See Also

Factorial  Permutations

Introduced in 2007
(6.0)