Tue 2017-12-26 08:03:44 UTC, BDesco:
>
> for n=3. I get binomial(-1,0) = 1
> I don't know why.

You can look at the documentation of binomial:

    sage: binomial?

You will see it indicates that the definition is extended:

    We extend this definition to include cases when [...]

and as a result, for any numerical value of x,

     binomial(x, 0)

returns 1.

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