Bell Triangle

Author

Eric W. Weisstein
November 11, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/BellTriangle.nb.

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

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

Table

b[1,1]:=1
b[n_,1]:=b[n,1]=b[n-1,n-1]
b[n_,k_]:=b[n,k]=b[n-1,k-1]+b[n,k-1]

Table[b[n,k],{n,5},{k,n}]//ColumnForm

Row Sums

Sum[k StirlingS2[n,k],{k,0,n}]

Table[Sum[k StirlingS2[n,k],{k,0,n}],{n,10}]

Plus@@@Table[b[n,k],{n,10},{k,n}]