The equation should be
x ¨ ( t ) = ∑ n + 2 ∞ n ( n − 1 ) a n t n − 2 = ∑ n = 0 ∞ ( n + 2 ) ( n + 1 ) a n + 2 t n {\displaystyle {\ddot {x}}(t)=\sum _{n+2}^{\infty }n(n-1)a_{n}t^{n-2}=\sum _{n=0}^{\infty }(n+2)(n+1)a_{n+2}t^{n}}
Return to errata.