Nexus Number

Author

Eric W. Weisstein
March 7, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/NexusNumber.nb.

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

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

Sum

FullSimplify[Sum[Binomial[d+1,k]n^k,{i,0,d}],n>0&&d>0&&d∈Integers]

Table[-(n^(1+d))+(((1+n))^(1+d)),{d,0,4}]//Expand//TraditionalForm

Table[-(n^(1+d))+(((1+n))^(1+d)),{d,0,4},{n,0,10}]//ColumnForm