Consider the equation

$u_t={}^2{u}_{},0x,t0$

with ${}^2=2,$ initial condition $u(x,0)=cos(\frac{x}{2})$ and boundary conditions

$u_x(0,t)=u_x(,t)=0.$ The Fourier series solution is of the form

$u(x,t)=\frac{a_0}{2}+{\displaystyle \underset{n=1}{\overset{}{}}}{a}_{n}cos(nx)e^{-2n^{2}t}$

Find a formula for the coefficients $a_n.$ Enter the formula as a Python function called with

input parameter $n.$