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I want to solve these recurrence relations with the initial conditions given. I know how to solve linear non-homogeneous recurrence relations with constant coefficients.

$$(a)\ \ {a_n}^2=2{a_{n-1}}^2+1 ,a_0=1$$ $$(b)\ \ a_n=-n a_{n-1}+n!,a_0=1$$

3 Answers 3