  Rota used the functional L to recover old properties and obtain some new
formulas for the Bell numbers. Tanny used Rota's functional L and the
celebrated Worpitzky identity to obtain some expression for the ordered Bell
numbers, which can be seen as an evident to the fact that the ordered Bell
numbers are gamma-positive. In this paper, we extend some of Rota's and Tanny's
results to the framework of the set partitions of Coxeter type B.
