$$(1 + x + x^2)^n = \sum_{k = 0}^{2n} a_kx^k \Rightarrow \sum_{k = 1}^n a_{2k - 1} =$$

A

$$\frac{1}{2}(3^{2n} + 1)$$

B

$$\frac{1}{2}(3^{n} + 1)$$

C

$$\frac{1}{2}(3^{n} - 1)$$

D

$$\frac{1}{2}(3^{2n} - 1)$$