This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111866 #5 Oct 31 2013 12:17:32
%S A111866 1,1,2,6,3,15,5,35,35,105,7,77,77,1001,143,429,2145,36465,12155,
%T A111866 230945,46189,323323,29393,676039,676039,16900975,1300075,2340135,
%U A111866 334305,9694845,215441,6678671,100180065,3305942145,64822395,2268783825
%N A111866 Divide n! repeatedly by i! for i from floor(n/2) down through 2; a(n) = remaining quotient.
%e A111866 a(9): 9!/(4!*4!*3!) = 105.
%t A111866 f[n_] := Block[{k = Floor[n/2], m = n!}, While[k > 1, While[ Mod[m, k! ] == 0, m /= k! ]; k-- ]; m]; Table[ f[n], {n, 0, 35}] (* _Robert G. Wilson v_ *)
%o A111866 (PARI) a(n)=c=n!;forstep(d=floor(n/2),2,-1, while (c%(d!)==0,c/=d!));c
%Y A111866 Cf. A055773.
%K A111866 nonn
%O A111866 0,3
%A A111866 _Jon Perry_, Nov 23 2005
%E A111866 More terms from _Robert G. Wilson v_, Nov 25 2005