In[]:=
Series[Exp[1/{z-z^{-1}}],{z,0,10},Assumptions{0<Abs[z]<infty}]
Out[]=
1-z+-+-+-+-++
2
z
2
7
3
z
6
25
4
z
24
181
5
z
120
1201
6
z
720
10291
7
z
5040
97777
8
z
40320
202709
9
z
72576
1743223
10
z
518400
11
O[z]
Out[]=
{}
infty
0
2
sum_
Out[]=
2.07045-0.0177716
In[]:=