A005394 Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded to nearest integer.

0, 1, 2, 6, 24, 118, 710, 4980, 39902, 359537, 3598696, 39615625, 475687486, 6187239475, 86661001741, 1300430722199, 20814114415223, 353948328666101, 6372804626194309, 121112786592293963, 2422786846761133394, 50888617325509644403, 1119751494628234263302

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000142, A090583.

Programs

Magma

R:= RealField(); [Round(Sqrt(2*Pi)*Exp(-n)*n^(n + 1/2)): n in [0..100]]; // G. C. Greubel, Aug 16 2018

Maple

a:= n-> round(sqrt(2*Pi*n)*(n/exp(1))^n):
seq(a(n), n=0..23);  # Alois P. Heinz, Jan 24 2024

Mathematica

Table[Round[Sqrt[2*Pi]*Exp[-n]*n^(n + 1/2)], {n, 0, 100}] (* G. C. Greubel, Aug 16 2018 *)

Extensions

Corrected and extended by Hugo Pfoertner, Jan 10 2004