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Sum of recurring numbers

Suppose $$n(n+1)a_{n+1}=n(n-1)a_n-(n-2)a_{n-1}$$

for each constructive integer. Given away $$a_0=1,a_1=3$$,discover the all sever of:

$$frac{a_0}{a_1}+frac{a_1}{a_2}+frac{a_2}{a_3}+frac{a_3}{a_4}+…+frac{a_{50}}{a_{51}}$$

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