Thread: Recurrence Relation View Single Post

## Recurrence Relation

1. The problem statement, all variables and given/known data
Got this recurrence relation when trying to solve for a series solution to a differential equation: $$a_n=\frac{a_{n-5}}{n(n-1)} , a_0,a_1=constant , a_2,a_3,a_4=0$$

2. Relevant equations

3. The attempt at a solution
My attempt at a solution involved first writing out all the terms which led to the pattern $$a_5=\frac{a_0}{5\cdot4}$$ and $$a_6=\frac{a_1}{6\cdot5}$$ and $$a_{10}=\frac{a_0}{10\cdot9\cdot5\cdot4}...a_{15}=\frac{a_0}{15\cdot14\c dot10\cdot9\cdot5\cdot4}$$

I ended up with $$a_n=\frac{a_0}{5^n \cdot n!}$$ missing something on the bottom which as far as I can tell is $$(5(n)-1)(5(n-1)-1)(5(n-2)-1)...$$
The problem is that i can't figure out a more concise simple expression for this last part. Any help would be greatly appreciated!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
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