Series-Parallel Network

Author

Eric W. Weisstein
November 8, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/Series-ParallelNetwork.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Series-ParallelNetwork.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

b[1]:=1
b[n_]:=b[n]=Module[{p=Most/@DeleteCases[PartitionsJ[n],{___,1}]},
Plus@@Times@@@(MapIndexed[Binomial[b[#2[[1]]]+#1-1,#1]&,#]&/@p)
]

Enumeration

b/@Range[10]

Prepend[2b/@Range[2,10],1]