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

0,3

Links

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

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 *)

Prog

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

Crossrefs

Cf. A000142, A090583.

Sequence in context: A328442 A135106 A248837 * A095818 A369098 A264781

Adjacent sequences: A005391 A005392 A005393 * A005395 A005396 A005397

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Corrected and extended by Hugo Pfoertner, Jan 10 2004

Status

approved