This function's double version is actually smaller because it only includes odd or even numbers in the computation of its output.
The left or sub- version of this function counts the number of derangements of n objects. A conjecture of ErdÂ®s states that there are only three pairs of numbers (m, n) such that THIS(n) + 1 = m2. The Pochhammer symbol is also known as this function's    rising  type. The exponential type of this function is de ned by the recurrence relation an = nan−1 . This function's double version is actually smaller because it only includes odd or even numbers in the computation of its output. This function of n gives the number of permutations of n objects. For ten points, identify this function denoted by an exclamation point.
The left or sub- version of this function counts the number of derangements of n objects.
factorial