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 A122221 #29 Aug 29 2025 20:55:10
%S A122221 2,5,8,13,19,25,32,41,50,60,72,84,97,111,126,142,159,177,196,216,237,
%T A122221 259,282,306,330,356,383,410,439,469,499,531,563,597,631,667,703,740,
%U A122221 779,818,858,899,942,985,1029,1074,1120,1167,1215,1264,1314,1365,1417
%N A122221 Largest number k such that k! < (n!)^n.
%H A122221 Chai Wah Wu, <a href="/A122221/b122221.txt">Table of n, a(n) for n = 2..10000</a>
%F A122221 From Stirling's approximation, a(n) ~ n^2/2. A closer approximation for a(n) is n^2/2-c*n^2/log(n), where c = (1+log(0.5))/4 = A382854/2. - _Johann Peters_, Aug 23 2025
%e A122221 a(3)=5 because 5! = 120 is less than (3!)^3 = 216 whereas 6! = 720 > 216.
%p A122221 a:=proc(n) local b: b:=proc(k) if k!<(n!)^n then k else fi end: max(seq(b(k),k=1..2200)) end: seq(a(n),n=2..67); # _Emeric Deutsch_, Oct 07 2006
%t A122221 s={};Do[k=1;Until[k!>=(n!)^n,k++]; AppendTo[s,k-1],{n,2,54}];s (* _James C. McMahon_, Oct 26 2024 *)
%Y A122221 Cf. A036740, A121347, A122222, A382854.
%K A122221 nonn,changed
%O A122221 2,1
%A A122221 _Hugo Pfoertner_, Sep 25 2006
%E A122221 More terms from _Emeric Deutsch_, Oct 07 2006