In[509]:= Table[Binomial[-1, k], {k, -3, 3}] Out[509]= {1, -1, 1, 1, -1, 1, -1} But In[550]:= Table[Binomial[m1, k], {k, -3, 3}] Out[550]= {0, 0, 0, 1, m1, 1/2 (-1 + m1) m1, 1/6 (-2 + m1) (-1 + m1) m1} In[551]:= % /. m1 -> -1 Out[551]= {0, 0, 0, 1, -1, 1, -1} Macsyma, since 40 years, (c1) makelist(binom(-1,k),k,-3,3) (d1) [0, 0, 0, 1, - 1, 1, - 1] I expect as much from Maple. Mma Doc: "As a bivariate function, Binomial is not continuous in both variables at negative integers: In[1]:= Binomial[-3, -5] Out[1]= 0 In[2]:= Binomial[-3.0000001, -5.0000001] Out[2]= 6. " But in inconvenient fact, In[552]:= Binomial[-3, -5] Out[552]= 6 I don't see how this eluded their test suite unless the latter is corrupted. Mma Doc: "In general, (n m) is defined by \[CapitalGamma] (n+1)/(\[CapitalGamma](m+1)\[CapitalGamma](n-m+1)) or suitable limits of this." For the record, these limits are Limit[Limit[x!/(y!*(x-y)!),y->m],x->n] This is how the bilateral symmetry of Pascal's triangle breaks down, even though the surface x!/(y!*(x-y)!) (appropriately skewed) is bilaterally symmetric. (I have repeatedly failed to make a convincing plot of this.) For anyone still doubting the symmetry breakdown for negative integer n: The recurrence that generates each row of Pascal's Triangle from the previous would place a "2" at the apex (0,0), if Out[509] were correct! --rwg Here is an almost correct technique for printing number triangles, of which Julian must repeatedly remind me: pt[n_Integer, from_Integer: 0] := TableForm[Table[If[EvenQ[i + j], "", Binomial[-1 + i, -Floor[n/4] + (1 + i + j)/2] /. 0 -> ""], {i, from, n}, {j, -Ceiling[3*n/4], n + 1}]] 10 -4 1 1 -4 6 -3 1 1 -3 6 -4 3 -2 1 1 -2 3 -1 1 -1 1 1 -1 1 -1 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 (Assuming GMail hasn't murdered it,) the upper left wedge is the spurious subject of this message. Pascal's Triangle is really Pascal's biwedge. NOT Pascal's Radiation Warning.