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A090583 Gosper's approximation to n!, sqrt((2*n+1/3)*Pi)*n^n/e^n, rounded to nearest integer. 5
1, 1, 2, 6, 24, 120, 720, 5039, 40316, 362851, 3628561, 39914615, 478979481, 6226774954, 87175314872, 1307635379670, 20922240412500, 355679137660826, 6402240370021199, 121642823201649058, 2432860847996122437, 51090157192742729183, 1123984974735953018069 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..449 (terms 0..200 from Alois P. Heinz)

Peter Luschny, Approximations to the Factorial Function.

Eric Weisstein's World of Mathematics, Stirling's Approximation. Section in World of Mathematics.

MAPLE

Digits:= 2000;

a:= n-> round(sqrt((2*n+1/3)*Pi)*n^n/exp(n)):

seq(a(n), n=0..30); # Alois P. Heinz, Feb 04 2013

MATHEMATICA

Join[{1}, Table[Round[Sqrt[(2*n + 1/3)*Pi]*n^n/Exp[n]], {n, 1, 50}]] (* G. C. Greubel, Nov 28 2017 *)

PROG

(PARI) a(n) = round(sqrt((2*n+1/3)*Pi)*n^n/exp(n)); \\ Bill McEachen, Aug 16 2014

(Magma) C<i> := ComplexField(); [Round(Sqrt((2*n + 1/3)*Pi(C))*n^n/Exp(n)): n in [0..30]]; // G. C. Greubel, Nov 28 2017

CROSSREFS

Cf. A000142, A005394, A055775.

Sequence in context: A248839 A052399 A177553 * A248775 A108889 A248772

Adjacent sequences: A090580 A090581 A090582 * A090584 A090585 A090586

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Jan 10 2004

STATUS

approved

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Last modified December 9 17:46 EST 2022. Contains 358703 sequences. (Running on oeis4.)