A229495 Stirling's approximation constant e / sqrt(2*Pi).

1, 0, 8, 4, 4, 3, 7, 5, 5, 1, 4, 1, 9, 2, 2, 7, 5, 4, 6, 6, 1, 1, 5, 7, 7, 3, 1, 3, 4, 2, 2, 9, 4, 7, 9, 8, 5, 8, 3, 9, 5, 9, 6, 9, 3, 1, 9, 6, 4, 7, 2, 6, 2, 6, 8, 2, 2, 5, 1, 3, 4, 3, 4, 7, 1, 2, 2, 8, 7, 5, 1, 4, 7, 9, 6, 2, 6, 9, 0, 0, 2, 4, 9, 9, 0, 3, 4, 7, 1, 6, 8, 2, 8, 8, 4, 8, 4, 7, 5, 3, 1, 5, 2, 3, 6, 6, 7, 9, 3, 9, 1, 9, 7, 3, 4, 9, 3, 6, 4, 3, 5, 3, 4, 7, 6, 8, 3, 8, 1, 5, 4, 1, 3, 1, 9, 5, 6, 3, 3, 6, 6, 3, 3, 4, 2, 9, 5, 1, 9, 7

Offset

1,3

References

Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 1.5, pages 2 and 27-28.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Wikipedia, Stirling's approximation.

Formula

Equals exp(1)/sqrt(2*Pi).

Equals lim_{n->oo} (A001142(n)^(1/n)*sqrt(n)/(exp(n/2))) (Furdui, 2013). - Amiram Eldar, Mar 26 2022

Equals Product_{n>=1} (1 + 1/n)^(n+1/2)/e. - Amiram Eldar, Jul 08 2023

Example

1.0844375514192275466115773134229479858...

Maple

evalf(exp(1)/sqrt(2*Pi), 120); # Muniru A Asiru, Oct 07 2018

Mathematica

RealDigits[E/Sqrt[2Pi], 10, 120][[1]] (* Harvey P. Dale, Jan 21 2017 *)

Prog

(PARI) exp(1)/sqrt(2*Pi) \\ Ralf Stephan, Sep 26 2013
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(1)/Sqrt(2*Pi(R)); // G. C. Greubel, Oct 06 2018

Crossrefs

Cf. A001113 (e), A019727 (sqrt(2*Pi)), A001142.

Sequence in context: A244091 A197033 A245720 * A370198 A131921 A129105

Adjacent sequences: A229492 A229493 A229494 * A229496 A229497 A229498

Keyword

nonn,cons

Author

John W. Nicholson, Sep 24 2013

Extensions

More terms from Ralf Stephan, Sep 26 2013

Corrected and extended by Harvey P. Dale, Jan 21 2017

Status

approved