A Big Fraction

$a_{1}=\frac12={\color{#D61F06}\frac12},\qquad a_{2}=\dfrac{\hspace{2mm} \frac12 \hspace{2mm} }{\hspace{2mm} \frac34\hspace{2mm} }={\color{#D61F06}\frac{1\times4}{2\times3}}, \qquad a_{3}=\dfrac{\hspace{2mm} \dfrac{\hspace{2mm} \frac12\hspace{2mm} }{\hspace{2mm} \frac34\hspace{2mm} }\hspace{2mm} }{\dfrac{\hspace{2mm} \frac56\hspace{2mm} }{\hspace{2mm} \frac78\hspace{2mm} }}={\color{#D61F06}\frac{1\times4\times6\times7}{2\times3\times5\times8}}$ The sequence $a_n \, (n=1, 2, 3, ...)$ goes on like the above, forming a really large fraction. Look at the final fractions (red ones), where 1 is always a part of the numerator, 2 a part of the denominator, 3 a part of the denominator $($ starting from $a_3),$ and so on: ${\color{#D61F06}\frac{\hspace{2mm} 1\times4\times6\times7\times10\times11\times\cdots\hspace{2mm} }{2\times3\times5\times8\times9\times12\times\cdots}}.$ Will 2018 always be a part of the numerator or denominator?