func left_factorial(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
}