How to solve this recurrence relation using generating functions?

by Dimitris Prasakis   Last Updated February 11, 2019 10:20 AM

How can we solve the following recurrence relation using GF?

$a_n = 10*a_{n-1}-25*a_{n-1} + 5^n*{n+2 \choose 2}$

I think that most of it is pretty straightforward. What really concerns me is this part

$5^n{n+2 \choose 2}$

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