Gould polynomials

In mathematics the Gould polynomials G_n(x; a,b) are polynomials introduced by H. W. Gould and named by Roman (1984, p.67) They are given by

$\displaystyle \exp(xf(t)) = \sum_nG_n(x;a,b)t^n/n!$

where

$f(t)=\sum_{k\ge 1} \frac{1}{b}\binom{-(b%2Bak)/b}{k-1}\frac{t^k}{k!}$

References

Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics, 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-594380-2, MR 741185, Reprinted by Dover, 2005, http://books.google.com/books?id=JpHjkhFLfpgC
Gould, H. W. (1961), "A series transformation for finding convolution identities", Duke Math. J. Volume 28, Number 2, 193-202.