Gould polynomials

In mathematics the Gould polynomials G_n(x; a,b) are polynomials introduced by H. W. Gould and named by Roman in 1984.^[1] They are given by ^[2]

${\displaystyle \displaystyle \exp(xf^{-1}(t))=\sum _{n=0}^{\infty }G_{n}(x;a,b){\frac {t^{n}}{n!}}}$

where

${\displaystyle f(t)=e^{at}(e^{bt}-1)}$ so ${\displaystyle f^{-1}(t)={\frac {1}{b}}\sum _{k=1}^{\infty }{\binom {-(b+ak)/b}{k-1}}{\frac {t^{k}}{k}}}$