(42S) Subfactorial

[Albert Chan]

(09-06-2021 06:50 PM)John Keith Wrote:  A simpler formula for the first program is a(n) = (n-1)*(a(n-1) + a(n-2)). Maybe not as easy to implement with a 4-level stack because you have to keep the two previous values to compute the current one.

We can use https://mathworld.wolfram.com/Subfactorial.html, #5

!n = n * !(n-1) + (-1)^n

Code:

def subfac(n, r=0):     # integer n > 0
    for i in range(2,n+1): r = 1-i*r
    return abs(r)