x0=0	f0=f[x0]=5
					f[x0,x1]=(9-5)/(1-0)=4
x1=1	f1=f[x1]=9							f[x0,x1,x2]=(6-4)/(2-0)=1
					f[x1,x2]=(15-9)/(2-1)=6									f[x0,x1,x2,x3]=(-3/2-1)/(3-0)=-5/6
x2=2	f2=f[x2]=15							f[x1,x2,x3]=(3-6)/(3-1)=-3/2
					f[x2,x3]=(18-15)/(3-2)=3
x3=3	f3=f[x3]=18


In veelterm:

f[x0,x1,x2,x3]*(x-0)*(x-1)*(x-2) = -13/12 * (x-0) * (x-1) * (x-2) =  -5/6 * (x^3 - 3x^2 +2x)
Term a3 -> -5/6 * x^3

f[x0,x1,x2,x3,x4]*(x-0)*(x-1)*(x-2)*(x-3) = 1 * (x-0) * (x-1) * (x-2) * (x-3) =  1 * (x^4 - 6x^3 + 11x^2 -6x)
Term a3 ->  - 6 * x^3

(-5/6 * x^3) +  (- 6 * x^3) = (-41/6 * x^3)
-> a3 = -41/6