Pidduck polynomials

In mathematics, the Pidduck polynomials s_n(x) are polynomials introduced by Pidduck^[1][2] given by the generating function

${\displaystyle \displaystyle \sum _{n}{\frac {s_{n}(x)}{n!}}t^{n}=\left({\frac {1+t}{1-t}}\right)^{x}(1-t)^{-1}}$

^[3][4]