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A005393 Leading term of Stirling's approximation to n!, sqrt(2*Pi)*n^(n+(1/2))/e^n, rounded down. 2
0, 0, 1, 5, 23, 118, 710, 4980, 39902, 359536, 3598695, 39615625, 475687486, 6187239475, 86661001740, 1300430722199, 20814114415223, 353948328666100, 6372804626194309, 121112786592293963, 2422786846761133393, 50888617325509644403 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 13 07:30 EDT 2020. Contains 335676 sequences. (Running on oeis4.)