login
Difference between (n!)^n and the next smaller factorial.
1

%I #6 Oct 27 2024 03:13:12

%S 2,96,291456,18656179200,17668969095168000,67095201210572537856000000,

%T 6721833410207820593461922365440000000,

%U 75658161802407509372174837302453333917696000000000,365526772920711815200262962616603688918661180831039488000000000000

%N Difference between (n!)^n and the next smaller factorial.

%e a(3)=96 because the difference between (3!)^3=216 and the next smaller factorial 5!=120 is 96.

%t s={};m=1;Do[Until[m!>(n!)^n,m++];AppendTo[s,(n!)^n-(m-1)!],{n,2,10}];s (* _James C. McMahon_, Oct 26 2024 *)

%Y Cf. A036740, A121348, A122221.

%K nonn

%O 2,1

%A _Hugo Pfoertner_, Sep 25 2006

%E a(10) from _James C. McMahon_, Oct 26 2024