Number sequence

It only works for n=0 to n=10. That's great, but NOT what I am looking for.
I can't wait to hear the answer to this question---How do you know that it works for only n=0 to n=10? Do you know other values in the sequence that you are not telling us about? If yes, then tell us all the numbers you know and someone here will give you a polynomial that works for all the numbers that you supply.
 
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