A090583 Gosper's approximation to n!, sqrt((2*n+1/3)*Pi)*n^n/e^n, rounded to nearest integer.

1, 1, 2, 6, 24, 120, 720, 5039, 40316, 362851, 3628561, 39914615, 478979481, 6226774954, 87175314872, 1307635379670, 20922240412500, 355679137660826, 6402240370021199, 121642823201649058, 2432860847996122437, 51090157192742729183, 1123984974735953018069

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.

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