+4
There is a single sequence of integers \(a_2,a_3,a_4,a_5,a_6, a_7 \)such that \(\frac{a_2}{2!} + \frac{a_3}{3!} + \frac{a_4}{4!} + \frac{a_5}{5!} + \frac{a_6}{6!} + \frac{a_7}{7!} = \frac{13}{42},\) and \(0 \le a_i < i \) for \( i = 2,3, \dots, 7.\)Find \(a_2,a_3,a_4,a_5,a_6,a_7.\)
