
The q-Deformed Weyl Algebra and the Meromorphic Weyl Algebra 265
Comparing this with (7.83), we obtain A
kn
= Sm
−1
(n, k). By (8.71), we obtain the first
explicit expression for the meromorphic Stirling numbers,
Sm
h
(n, k)=
−
h
2
n−k
−n
n −k
(n − 1)!
(k − 1)!
.
Comparing (7.84) with the definition of Lang’s generalized Stirling numbers S(r; n, k)in
[710] reveals that Sm
−1
(n, k)=|S(−1; n, k)|, and the latter count unordered k-forests of
ordered rooted increasing trees with vertices of any out-degree where there are n vertices
altogether [712]; see also A132026 in [1019]. Another interpretation can be found by recalling
Theorem 7.48, thereby identifying Sm
h
(n,