three binomial(n,k) definitions

[Michael Somos]

seqfan,

I previously wrote :

>       fibonacci(n)=sum(binomial(n-k,k))

without any numerical check. It is incorrect. My corrected work :

> C(n, k) = if(k>n,0,if(k<0,(-1)^(n+k)*C(-1-k,n-k),n!/k!/(n-k)!))
> ? oo=100;print(prod(n=-oo,oo,fibonacci(n+1)==sum(k=-oo,oo,C(n-k,k))))
> 1

which shows how careful you have to be. Shalom, Michael