Abstract
The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper exhibits the number of support-tilting modules for any Dynkin algebra. Since the support-tilting modules for a Dynkin algebra of Dynkin type A correspond bijectively to the generalized non-crossing partitions of type A, the calculations presented here may also be considered as a categorification of results concerning the generalized non-crossing partitions. In the Dynkin case A, we obtain the Catalan triangle, in the cases 13 and C the increasing part of the Pascal triangle, and finally in the case TED an expansion of the increasing part of the Lucas triangle.