Define a sequence {a_n} as follows:

a_0 = 2, a_1 = 3, a_2 = 6

and, for n ≥ 3,

a_n = (4+n) a_{n-1} – 4n a_{n-2} + (4n -8) a_{n-3}.

Thus, the first several values are 2, 3, 6, 14, 40, 152, 784, and 5168.

Find and prove a formula of the form a_n = b_n + c_n where {b_n} and {c_n} are common sequences!

**Hint: **b_n = 2^n and c_n = n!