# Ink on Sequences #2

Calculus Level 5

For every positive integer $$n$$, let a sequence $$\{a_n\}$$ satisfy:

$\large \begin{cases} a_{2n+1}=a_{2n-1}+2n-1 \\ a_{2n+2}=na_{2n} \end{cases}$

Find the value of $$\displaystyle \lim_{n\rightarrow\infty}\frac{12a_{2n}a_{2n+9}}{a_6\cdot(n+1)!}$$.

This problem is a part of <Inconsequences!> series.

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