Bracketing

Author

Eric W. Weisstein
April 15, 2004

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

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

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

Series

Series[(1+x-Sqrt[1-6x+x^2])/4,{x,0,10}]

Recurrence

s[1]:=1
s[2]:=1
s[n_]:=s[n]=(3(2n-3)s[n-1]-(n-3)s[n-2])/n

Table[s[n],{n,10}]

v4.2

<<DiscreteMath`RSolve`

RSolve[{s[n]n==3(2n-3)s[n-1]-(n-3)s[n-2],s[1]==1,s[2]==1},s[n],n]

Simplify[(1/4) If[n==1,1,0]+(1/4) (-If[n≥0,LegendreP[n,3],0]+6 If[n≥1,LegendreP[-1+n,3],0]-If[n≥2,LegendreP[-2+n,3],0]),n>2]//FullSimplify

v5

RSolve[{s[n]n==3(2n-3)s[n-1]-(n-3)s[n-2],s[1]==1,s[2]==1},s[n],n]