The result looks like, f(x) = a1 + C(x,1)*a2 + C(x, 2) * a3…..C(x,n-1) * an

Here C(n,c) is the binomial coefficient. a1, a2… an are the given numbers in the first column.

Technically speaking in my formula f(0) will be the first term and not f(1). I hope that does not matter. Otherwise I just need to use (x-1) in place of x and will make the formula ugly. By the way, is there are better simplification than this? Not sure.