Excellent, thanks! rwg> Modulo shifting by 1, Out[1157]= -(-1)^n 2^(-1+2 n) Binomial[1/2,n] In[1158]:= Table[%,{n,9}] Out[1158]= {1,1,2,5,14,42,132,429,1430} In[1161]:= Sum[%1157*x^n,{n,\[Infinity]}] Out[1161]= 1/2 (1-Sqrt[1-4 x]) In[1162]:= Sum[x^n/%1157,{n,\[Infinity]}] Out[1162]= x Hypergeometric2F1[1,2,1/2,x/4] In[1163]:= FunctionExpand[%] Out[1163]= x ((2+x/4)/(2 (-1+x/4)^2)+(3 Sqrt[x] ArcCsc[2/Sqrt[x]])/(4 Sqrt[1-x/4] (-1+x/4)^2)) In[1164]:= FullSimplify[%,0<x<1] Out[1164]= (2 x (Sqrt[4-x] (8+x)+12 Sqrt[x] ArcCsc[2/Sqrt[x]]))/(4-x)^(5/2) In[1165]:= Series[%,{x,0,9}] Out[1165]= x+x^2+x^3/2+x^4/5+x^5/14+x^6/42+x^7/132+x^8/429+x^9/1430+O[x]^10 --rwg -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com