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## Main Question or Discussion Point

I'm finding a solution to and ODE using a Frobenius form solution, I have worked through the question and have ended up with a recurrence of the form;

a(k) = -2/(2k-1) a(k-1)

I'm trying to find a general reccurence in terms of a(0) but am finding it a bit difficult, I know it has to have a (2n-1)! term on the bottom of the fraction and a (-2)^(n) term on top but I'm a bit stuck as to where to go after this.

Sorry I haven't Latex-ed anything, I don't know how!

Any help would be fantastic, thanks.

a(k) = -2/(2k-1) a(k-1)

I'm trying to find a general reccurence in terms of a(0) but am finding it a bit difficult, I know it has to have a (2n-1)! term on the bottom of the fraction and a (-2)^(n) term on top but I'm a bit stuck as to where to go after this.

Sorry I haven't Latex-ed anything, I don't know how!

Any help would be fantastic, thanks.