Ak[_,1]=2;Ak[0,x_]:=x+2;Ak[n_,x_]:=Ak[n - 1, Ak[n, x - 1]] In[3]:= TableForm[Table[Ak[n,x],{n,0,3},{x,1,6-n}]] Out[3]//TableForm= 2 4 5 6 7 8 2 4 6 8 10 2 4 8 16 2 4 16 (Rows: n = 0,1,2,3; Columns: x = 1,2,3,4) Let's try bumping the row length. In[4]:= TableForm[Table[Ak[n,x],{n,0,3},{x,1,7-n}]] During evaluation of In[4]:= $RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of 1-1. >> One minus one? It's trying for 65536 by adding up 2s recursively. Let's give it a hint: In[2]:= Ak[1,x_]:=2x In[3]:= TableForm[Table[Ak[n,x],{n,0,3},{x,1,7-n}]] Out[3]//TableForm= 2 4 5 6 7 8 9 2 4 6 8 10 12 2 4 8 16 32 2 4 16 65536 Trying for one more x, In[5]:= TableForm[Table[Short[Ak[n,x]],{n,0,3},{x,1,8-n}]] During evaluation of In[5]:= $RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of 2-1. >> Out[5]//TableForm= 2 4 5 6 7 8 9 10 2 4 6 8 10 12 14 2 4 8 16 32 64 2 4 16 65536 2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 (2 MaxFormatDepthExceeded MaxFormatDepthExceeded MaxFormatDepthExceeded)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Time for another hint: In[7]:= Ak[2,x_]:=2^x In[8]:= TableForm[Table[Short[Ak[n,x]],{n,0,3},{x,1,8-n}]] Out[8]//TableForm= 2 4 5 6 7 8 9 10 2 4 6 8 10 12 14 2 4 8 16 32 64 2 4 16 65536 20035299304068464649790723<<19677>>72339445587895905719156736 (Insanely) trying for another row, In[9]:= TableForm[Table[Short[Ak[n, x]], {n, 0, 4}, {x, 1, 8 - n}]] $RecursionLimit::reclim2: Recursion depth of 1024 exceeded during evaluation of 3-1. >> (See nice try <http://gosper.org/ack.png>. Hey, where's the diagonal scroll bar?) --rwg