I'm doing some analysis which includes computing the sequence for some $f(t)$: $\left\{{f(t_0), \left.\frac{df}{dt}\right|_{t=t_0}}, \left.\frac{d^2f}{dt^2}\right|_{t=t_0}, \ldots ,\left.\frac{d^nf}{dt^n}\right|_{t=t_0} \right\}$, where n is some finite number. Given its strong connection to Taylor series and its really useful properties, I'm thinking it probably has been given a name, but I can't seem to find one.
Does that series have a well recognized name (such that I could search for it to find additional properties)