7个鸡蛋，放进3个不同的碗，允许有空碗，有多少种放法？

eggs.py

#!/usr/bin/env python
#coding=utf-8

# 7个鸡蛋，放进3个不同的碗，允许有空碗，有多少种放法？
#   use function `place` to get answer
#   and `place_non` for **avoid empty bowl**

def gen_counts(prev, cur):
    str =  f"{cur}" if prev == "" else f"{prev},{cur}"
    return str

def place(eggs, bowls, counts, lst):
    if bowls == 1:
        lst.append(gen_counts(counts, eggs))
        return 1
    if eggs == 0:
        lst.append(gen_counts(counts,0))
        return 1
    count = 0
    for i in range(eggs+1):
        cur_bowl_count = i
        str_counts = gen_counts(counts, cur_bowl_count)
        count += place(eggs-i, bowls-1, str_counts, lst)
    return count

def place_non(eggs, bowls, counts, lst):
    if bowls == 1:
        lst.append(gen_counts(counts, eggs))
        return 1
    count = 0
    for i in range(1,eggs-bowls+2):
        cur_bowl_count = i
        str_counts = gen_counts(counts, cur_bowl_count)
        count += place_non(eggs-i, bowls-1, str_counts, lst)
    return count

# utility
def str2bool(v):
    if isinstance(v, bool):
       return v
    if v.lower() in ('yes', 'true', 't', 'y', '1'):
        return True
    elif v.lower() in ('no', 'false', 'f', 'n', '0'):
        return False
    else:
        raise argparse.ArgumentTypeError('Boolean value expected.')

import argparse
parser = argparse.ArgumentParser(description='X eggs put into Y [avoid/allow] bowls, how many arrangements?')
parser.add_argument('X', nargs='?', default=7, type=int, help='the count of eggs')
parser.add_argument('Y', nargs='?', default=3, type=int, help='the count of bowls')
parser.add_argument('--avoid_empty_bowl', '-a', nargs='?', const=True, default=False, type=str2bool, help='if bowls can be empty')
def main():
    args = parser.parse_args()
    print(args)
    lst = []
    func = place
    if args.avoid_empty_bowl:
        func = place_non
    count = func(args.X, args.Y, "", lst)
    str_empty = "avoid" if args.avoid_empty_bowl else "allow"
    print(f"count for [{args.X}] eggs and [{args.Y}] [{str_empty} empty] bowls is: {count}")
    # lst.sort()
    for e in lst:
        print(f"  {e}")

if __name__ == "__main__":
    main()