Besides Warren's proposals, Dodgson's method is valuable theoretically, helping Rich prove my Somos addition formulæ http://arxiv.org/abs/math/0703470 and Zeilberger prove the famously challenging Alternating Sign Matrix Theorem (A005130), the "Stirling's formula" for which is Out[264]= (2^(5/12 - 2*n^2)*3^(-(7/36) + (3*n^2)/2)* E^((1/3)*HoldForm[Derivative[1][Zeta][-1]])*Pi^(1/3))/ (n^(5/36)*Gamma[1/3]^(2/3)) (the HoldForm to fend off that vexatious Glaisher symbol). In[265]:= Table[N[ReleaseHold[%]], {n, 9}] // InputForm Out[265]//InputForm= {1.0063254118710128, 2.003523267231662, 7.0056223910285915, 42.01915917750558, 429.12582410098327, 7437.518404899576, 218380.8077275304, 1.085146545456063*^7, 9.119184824937415*^8} the actual sequence being 1, 1, 2, 7, 42, 429, 7436, 218348, 10850216, 911835460, 129534272700, Adamchik may have already worked this out someplace, in spite of the painful obstacles thrown up by Mathematica. OEIS could probably use more such asymptotic formulæ. --rwg