Find the first five terms of the sequence as defined by these relations and the initial terms.
$A_n = nA_{n-1} + n^2 A_{n-2}$
$A_0 = 1$
$A_1 = 1$
$A_2 = 1\cdot 1 + 1^2 \cdot 1 = 2$
$A_3 = 3 \cdot 2 + 3 ^ 2 \cdot 1 = 15$
$A_4 = 4 \cdot 15 + 4 ^ 2 \cdot 2 = 96$
Answer sheet says I'm wrong. Where did I mess up here?
$A_2 = 1\cdot 1 + 1^2 \cdot 1 = 2$ is not correct. We have $A_2=2A_1+4A_0=6.$