count.py

from functools import lru_cache

coins= 10,20,50,100,200,500,1000,2000,5000,10000

@lru_cache(None)
def count(amount, idx=len(coins)-1):
    if amount < 0 or idx < 0: return 0
    if amount == 0: return 1
    return count(amount - coins[idx], idx) + count(amount, idx-1)

print(count(1000000))