Answer
\[
\boxed{1,\;1,\;2,\;7,\;33,\;191}
\]
Work Step by Step
Given the recurrence
\[
u_k = k\,u_{k-1} \;-\; u_{k-2}
\quad\text{for } k \ge 3,
\]
with
\[
u_1 = 1,\quad u_2 = 1,
\]
we can compute the first six terms step by step:
1. \(u_1 = 1\)
2. \(u_2 = 1\)
3. \(u_3 = 3\,u_2 - u_1 = 3 \cdot 1 - 1 = 2\)
4. \(u_4 = 4\,u_3 - u_2 = 4 \cdot 2 - 1 = 7\)
5. \(u_5 = 5\,u_4 - u_3 = 5 \cdot 7 - 2 = 35 - 2 = 33\)
6. \(u_6 = 6\,u_5 - u_4 = 6 \cdot 33 - 7 = 198 - 7 = 191\)
