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Solving a second-order differential equation using power series

I'm trying to solve (x^2 - 1)*y'' -2*y = 0

The answer I keeping coming with is:

c1*[-x - (2/3!)*x^3 - (8/5!)*x^5 - (144/7!)*x^7 - (6048/9!)*x^9 +...]

Does anyone see a pattern with respect to the numerators (2, 8, 144, 6048...)?
 
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