%I A008338
%S A008338 1,1,2,12,288,34560,48,241920,6,2177280,7900913664000,
%T A008338 315379190543155200000,658409472000,4099929477061017600000,47029248000,
%U A008338 61498942155915264000000,2939328000,1045482016650559488000000,163296000
%N A008338 a(n+1) = a(n)/n! if n! divides a(n) else a(n)*n!.
%D A008338 R. K. Guy and R. J. Nowakowski, Monthly unsolved problems, 1969-1995, 
               Amer. Math. Monthly, 102 (1995), 921-926.
%p A008338 A008338 := proc(n) option remember; if n = 1 then 1 elif A008338(n-1) 
               mod (n-1)! = 0 then A008338(n-1)/(n-1)! else A008338(n-1)*(n-1)!; 
               fi; end;
%t A008338 a[1] := 1; a[n_] := If[IntegerQ[a[n - 1]/(n - 1)! ], a[n - 1]/(n - 1)!, 
               a[n - 1]*(n - 1)! ]; Table[a[n], {n, 1, 20}] - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Apr 08 2006
%Y A008338 Sequence in context: A083568 A003121 A057170 this_sequence A000178 A108395 
               A009669
%Y A008338 Adjacent sequences: A008335 A008336 A008337 this_sequence A008339 A008340 
               A008341
%K A008338 nonn,easy,nice
%O A008338 1,3
%A A008338 N. J. A. Sloane (njas(AT)research.att.com).
%E A008338 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 08 2006