When $|x|>3$, the coefficient of $\frac{1}{x^n}$ in the expansion of $x^{3 / 2}(3+x)^{1 / 2}$ is

• A

  $(-1)^n \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{2^n n!} 3^n$
• Correct answer
  B

  $(-1)^{n+1} \frac{1 \cdot 3 \cdot 5 \ldots(2 n+1)}{2^{n+2}(n+2)!} 3^{n+2}$
• C

  $(-1)^{n+1} \frac{1 \cdot 3 \cdot 5 \ldots(2 n-1)}{2^n n!} 3^{n+1}$
• D

  $(-1)^{n+1} \frac{1 \cdot 3 \cdot 5 \ldots(2 n+1)}{2^{n+3}(n+2)!} 3^{n+1}$

Hence, the correct answer is option: 'B'.