We call a function $f(x)\in \mathbb{C}[[x]]$ $D-finite$ if there exists a differential operator of the from $$ a_{i}(x)(D_x)^i + \ldots+a_{0}(x) $$ which annihilated $f(x)$. $D_{x}=\frac{\partial}{\partial x}$ and $a_i (x)\in \mathbb{C}(x)$. For example $e^x=\sum_{d}\frac{1}{d!}x^d$ is D-finite.
I wanted to compute the Annihilator for the function
$$P(x):=1+ \sum_{d\geq1}\frac{1}{(\lfloor{\frac{d}{2}}\rfloor)!} x^{d} $$
where $\lfloor,\rfloor$ denote integer function for example $\lfloor5/2\rfloor=2$.
RISC could not compute the annihilator for it. Is this not a $D-finite$ function?