We give a possible definition of 2-admissible functions (one possible
generalization of Hayman-admissibility to bivariate functions) such
that the coefficients of
satisfy a central limit
theorem. One typical example is
,
where the coefficients are the Stirling numbers of the second kind.
We also provide a list of closure properties of these kind of 2-admissible functions which can be automatically checked with the help of a MAPLE program.