%I #13 Jan 24 2024 09:43:41
%S 0,1,2,6,24,118,710,4980,39902,359537,3598696,39615625,475687486,
%T 6187239475,86661001741,1300430722199,20814114415223,353948328666101,
%U 6372804626194309,121112786592293963,2422786846761133394,50888617325509644403,1119751494628234263302
%N Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded to nearest integer.
%H G. C. Greubel, <a href="/A005394/b005394.txt">Table of n, a(n) for n = 0..449</a>
%p a:= n-> round(sqrt(2*Pi*n)*(n/exp(1))^n):
%p seq(a(n), n=0..23); # _Alois P. Heinz_, Jan 24 2024
%t Table[Round[Sqrt[2*Pi]*Exp[-n]*n^(n + 1/2)], {n, 0, 100}] (* _G. C. Greubel_, Aug 16 2018 *)
%o (Magma) R:= RealField(); [Round(Sqrt(2*Pi)*Exp(-n)*n^(n + 1/2)): n in [0..100]]; // _G. C. Greubel_, Aug 16 2018
%Y Cf. A000142, A090583.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
%E Corrected and extended by _Hugo Pfoertner_, Jan 10 2004