Jonah Formula

Author

Eric W. Weisstein
September 21, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Definition

d[p_,k_]:=(1/k)Binomial[p k,k-1]

Special Value

d[2,k]

FullSimplify[((Binomial[2 k,-1+k])/k)]

FullSimplify[FunctionExpand[%]]

FullSimplify[d[2,k]-CatalanNumber[k]]

Identity

Sum[d[p,q i]Binomial[n-p i,j-i],{i,k}]

Table[{Sum[d[p,q i]Binomial[n-p i,j-i],{i,k}],Binomial[n-q,k-1]},{j,3},{k,3},{n,3},{p,3},{q,p-1}]