From: peter.luschny@gmail.com   
      
   Note that I considered above the case k=n.   
      
   But as it turns out this is by no means the only case   
   which reveals differences.   
      
   Consider now the case k = n-1: Alpha gives for   
      
   Table[2^(n-1)*Binomial[n-1,n-1]*Hypergeometric2F1[1,-n+1,-n+1,1/2],{n,0,9}]   
      
   | 1 | 1 | 3 | 7 | 15 | 31 | 63 | 127 | 255 | 511   
   (this time Mathematica gives the same results), but Maple   
      
   seq(evalf(2^(n-1)*binomial(n-1,n-1)*hypergeom([1,-n+1],[-n+1],1/2)), n=0..7);   
   1, 2, 4, 8, 16, 32, ...   
      
   Peter   
      
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