A005393 Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded down.

0, 0, 1, 5, 23, 118, 710, 4980, 39902, 359536, 3598695, 39615625, 475687486, 6187239475, 86661001740, 1300430722199, 20814114415223, 353948328666100, 6372804626194309, 121112786592293963, 2422786846761133393, 50888617325509644403

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..150

Wikipedia, Stirling's Approximation

Formula

a(n) = floor(sqrt(2*Pi)*n^(n+(1/2))/e^n). - Wesley Ivan Hurt, Jun 11 2016

Maple

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

Mathematica

Table[Floor[Sqrt[2*Pi]*n^(n + 1/2)*Exp[-n]], {n, 0, 50}] (* G. C. Greubel, Jun 11 2016 *)

Prog

(PARI) for(n=0, 50, print1(floor(sqrt(2*Pi)*n^(n+(1/2))*exp(-n)), ", ")) \\ G. C. Greubel, Aug 16 2018
(Magma) R:= RealField(); [Floor(Sqrt(2*Pi(R))*n^(n+(1/2))/Exp(n)): n in [0..50]]; // G. C. Greubel, Aug 16 2018

Crossrefs

Cf. (rounded up) A005395.

Sequence in context: A073596 A167248 A321798 * A193704 A294356 A162815

Adjacent sequences: A005390 A005391 A005392 * A005394 A005395 A005396

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

a(12) onwards corrected by Sean A. Irvine, Jun 11 2016

Status

approved