Given the sequence

,ask the value of
wikipedia: k-permutations of n are the different ordered arrangements of a k-element subset of an n-set (sometimes called
variations or
arrangements in the older literature). These objects are also known as partial permutations or as sequences without repetition, terms that avoid confusion with the other, more common, meaning of "permutation". The number of such
k-permutations of
n is denoted variously by such symbols as

or
_%7B%7D)
,and its value is given by the product
%3D%5Cunderbrace%20%7Bn%5Ccdot%20(n-1)%5Ccdot%20(n-2)%5Ccdots%20(n-k%2B1)%7D%20_%7Bk%5C%20%5Cmathrm%20%7Bfactors%7D%20%7D)
,which is

when

, and otherwise is equal to
!%7D%7D)
.
Assume that
%20%3D%201%2C%20P(0%2C%200)%20%3D%201_%7B%7D)