Hi Guys,
Question: what is closed formula for generating function 1 /(1-2x^2)?
Thanks
Chicago Boy
The Taylor expansion of $\displaystyle f(x)$ around $\displaystyle x=0$ is...
$\displaystyle f(x) = \frac{1}{1- 2\cdot x^{2}} = 1 + 2\cdot x^{2} + 4\cdot x^{4} + \dots + (2\cdot x^{2})^{n} + \dots = \sum_{n=0}^{\infty} (2\cdot x^{2})^{n} $ (1)
... where the series converges for $\displaystyle |x|< \frac{\sqrt{2}}{2}$, so that $\displaystyle f(x) = \frac{1}{1-2\cdot x^{2}}$ is the generating function of the sequence...
$\displaystyle a_{n}= 2^{\frac{n}{2}} $ n even, $\displaystyle a_{n}=0$, n odd
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$