Random termial with removed binomial coefficient

termial.py

#!/usr/bin/env python3
# Based on https://gist.github.com/fridex/8a2442f7e187914af715968097688aa3

import math
import random
import sys


def random_termial(n: int) -> int:
    """Get index to an item from a list of size n.

    The higher index of an item is, the lower probability of picking it.
    """
    assert n >= 1
    addition = (n * (n & 1))
    nearest = n + addition
    termial_of_n = ((1 + nearest) * (nearest >> 1)) - addition
    choice = random.randrange(termial_of_n)
    i = math.floor(-0.5 + math.sqrt(0.25 + (choice << 1)))
    return n - 1 - i


def main() -> None:
    if len(sys.argv) == 1:
        print(f"Usage: {sys.argv[0]} [N..]", file=sys.stderr)
        sys.exit(1)

    for item in sys.argv[1:]:
        n = int(item)   # Any exception reported.
        res = random_termial(n)
        print(f"Random index using random termial to a list of size {n} is {res}")


__name__ == "__main__" and main()