\frac{200 \sin \left(\frac{k \pi }{2}\right)}{k^2 \pi ^2}-\frac{50 \left(\pi ^2 \cos \left(\frac{k \pi }{2}\right) k^2-8 \cos \left(\frac{k \pi }{2}\right)+8\right)}{k^3 \pi ^3}