Gould polynomials

In mathematics the Gould polynomials Gn(x; a,b) are polynomials introduced by H. W. Gould and named by Roman in 1984. They are given by
 * $$ \displaystyle \exp(x f^{-1}(t)) = \sum_{n=0}^{\infty} G_n(x;a,b)\frac{t^n}{n!}$$

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