3 7 11 15 5 9 13 17
x x x x x x x x
x - -- - ---- - -------- - ------------- + --- + ------ + ---------- + ---------------
6 5040 39916800 1307674368000 120 362880 6227020800 355687428096000
$$\frac{x^{17}}{355687428096000} - \frac{x^{15}}{1307674368000} + \frac{x^{13}}{6227020800} - \frac{x^{11}}{39916800} + \frac{x^{9}}{362880} - \frac{x^{7}}{5040} + \frac{x^{5}}{120} - \frac{x^{3}}{6} + x$$
x - x^3/6 - x^7/5040 - x^11/39916800 - x^15/1307674368000 + x^5/120 + x^9/362880 + x^13/6227020800 + x^17/355687428096000