of the binomial coefficient formula: In[60]:= FindSequenceFunction[Factor[FindSequenceFunction[#,k]&/@NestList[Accumulate,Table[1,{9}],7]],n] Out[60]= Pochhammer[k, -1 + n]/Pochhammer[1, -1 + n] In[61]:= TableForm[Table[%, {n, 5}, {k, 5}]] Out[61]= 1 1 1 1 1 1 2 3 4 5 1 3 6 10 15 1 4 10 20 35 1 5 15 35 70 --rwg