func left_fact(n) {
    static cached    = 0
    static factorial = 1
    static leftfact  = 0
 
    if (n < cached) {
        cached    = 0
        factorial = 1
        leftfact  = 0
    }
 
    while (n > cached) {
        leftfact  += factorial
        factorial *= ++cached
    }
 
    leftfact
}