- #1

- 19

- 0

[tex]a_{n+2}=\frac{(n+3)a_{n}}{2(n+2)(n+1)}[/tex]

I found that the even coefficients work out nicely to the following sum:

[tex]y=a_{0}+\Sigma^{\infty}_{n=2}\frac{(n+1)a_{0}}{4*6^{n-2}}x^{n}[/tex]

I couldn't get a nice result for the odd coefficients and still can't find one. It's kind of bothering me now. Is it even possible? I can boil it down to this series:

[tex]\frac{1}{3},\frac{1}{20},\frac{1}{210},\frac{1}{3024},\frac{1}{55440},...[/tex]