  For delta operator $aD-bD^{p+1}$ we find the corresponding polynomial
sequence of binomial type and relations with Fuss numbers. In the case
$D-\frac{1}{2}D^2$ we show that the corresponding Bessel-Carlitz polynomials
are moments of the convolution semigroup of inverse Gaussian distributions. We
also find probability distributions $\nu_{t}$, $t>0$, for which
$\left\{y_{n}(t)\right\}$, the Bessel polynomials at $t$, is the moment
sequence.
