z-transform of nk


0 1 2 3 4 5 6 7
1              
1 1 0 0 0 0 0 0
1 4 1 0 0 0 0 0
1 11 11 1 0 0 0 0
1 26 66 26 1 0 0 0
1 57 302 302 57 1 0 0
1 120 1191 2416 1191 120 1 0
1 247 4293 15619 15619 4293 247 1



References:
Eliahu I. Jury, Theory and Application of the Z-transform Method, 1964
Jon M. Smith, Mathematical Modeling & Digital Simulation, p.307.