Find the Nth Term $a _ { n }$ Of a Sequence Whose First Four Terms Are Given

Find the nth term $a _ { n }$ of a sequence whose first four terms are given.
- $\frac { 1 \cdot 2 \cdot 3 \cdot 4 } { 2 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 } { 4 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 } { 6 } , \frac { 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 } { 8 } , \ldots$

A) $a _ { n } = \frac { ( n + 4 ) ! } { 2 ^ { n } }$
B) $a _ { n } = \frac { ( n + 4 ) ! } { 2 n }$
C) $a _ { n } = \frac { ( n + 3 ) ! } { 2 n }$
D) $a _ { n } = \frac { ( n + 3 ) ! } { 2 ^ { n } }$