Convert coefficients from interpolated newton-polynomial to c0 +c1*x + c2*x^2 + ... form

Hello,

I have interpolated x1..xi, y1..yi with a newton-polynomial, which gives me

p = c0 + c1(x-x1) + c2(x-x1)(x-x2) + ...

Now I want to comvert this polynomial to a polynomial of the form

p = d0 + d1*x + d2*x^2 + d3*x^3 + ...

What formula or algoritm can I use to convert the c0, c1... to d0, 
d1..., to get the same polynominal?

Thanks in advance,
Carl