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%I #16 Sep 08 2022 08:44:33
%S 0,0,1,5,23,118,710,4980,39902,359536,3598695,39615625,475687486,
%T 6187239475,86661001740,1300430722199,20814114415223,353948328666100,
%U 6372804626194309,121112786592293963,2422786846761133393,50888617325509644403
%N Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded down.
%H G. C. Greubel, <a href="/A005393/b005393.txt">Table of n, a(n) for n = 0..150</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Stirling%27s_approximation">Stirling's Approximation</a>
%F a(n) = floor(sqrt(2*Pi)*n^(n+(1/2))/e^n). - _Wesley Ivan Hurt_, Jun 11 2016
%p A005393:=n->floor(sqrt(2*Pi)*n^(n+(1/2))/exp(1)^n): seq(A005393(n), n=0..30); # _Wesley Ivan Hurt_, Jun 11 2016
%t Table[Floor[Sqrt[2*Pi]*n^(n + 1/2)*Exp[-n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 11 2016 *)
%o (PARI) for(n=0,50, print1(floor(sqrt(2*Pi)*n^(n+(1/2))*exp(-n)), ", ")) \\ _G. C. Greubel_, Aug 16 2018
%o (Magma) R:= RealField(); [Floor(Sqrt(2*Pi(R))*n^(n+(1/2))/Exp(n)): n in [0..50]]; // _G. C. Greubel_, Aug 16 2018
%Y Cf. (rounded up) A005395.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_
%E a(12) onwards corrected by _Sean A. Irvine_, Jun 11 2016
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