In following, $x_{n}$ is a set of given numbers, n = 0, 1, 2, ...,

$y_{n}$ is defined by the following recursive relation of $x_{n}$:

For example:

${\displaystyle {x_{1}=x_{0}y_{1} }}.$

${\displaystyle {x_{2}={\binom {1}{0}}x_{0}y_{2} + {\binom {1}{1}}x_{1}y_{1} }}.$

${\displaystyle {x_{3}={\binom {2}{0}}x_{0}y_{3} + {\binom {2}{1}}x_{1}y_{2} + {\binom {2}{2}}x_{2}y_{1} }}.$

For simplicity, we can assume $x_{0} = 1$.

Q1: Is there an explicit solution of $y_{n}$ in term of $x_{n}$ ?

Q2: I assume that above relation should be well known, is it a name for such relation ?

Thank you.