k=4
syms x;
f=x;
for i=2:k
     f=f+1/factorial(i)*x^i;
end
f2 = f;
for i=2:k
    f2=f2+(-1)^(i+1)/i*f^i;
end
disp(k)
disp(expand(f2))

- x^16/1327104 - x^15/82944 - x^14/9216 - (29*x^13)/41472 - (71*x^12)/20736 - (23*x^11)/1728 - x^10/24 - (541*x^9)/5184 - (239*x^8)/1152 - (5*x^7)/16 - (47*x^6)/144 - (5*x^5)/24 + x