On a generalised stirling distribution

In this note we consider a generalisation of theStirling noumber of the second kind. The distribution of the sum ofn independent zero-truncated Poisson variables, which can be expressed in terms of such a gneralised number, may be called horizontally generalised Stirling distribution of the second kind. A recurrence relation for the probability function of this distribution, which will be useful for tabulation purposes, is given. The distribution function is obtained in terms of a linear combination of incomplete gamma functions.