This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A229495 #36 May 30 2025 08:03:43
%S A229495 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,
%T A229495 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,
%U A229495 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
%N A229495 Stirling's approximation constant e / sqrt(2*Pi).
%D A229495 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.
%H A229495 G. C. Greubel, <a href="/A229495/b229495.txt">Table of n, a(n) for n = 1..10000</a>
%H A229495 Rafael Jakimczuk, <a href="http://dx.doi.org/10.13140/RG.2.2.13911.18084">Two Topics in Number Theory: Products Related with the e Number and Sum of Subscripts in Prime Numbers</a>, ResearchGate, May 2025. See p. 2, the constant exp(C) in eq. (2.1).
%H A229495 Wikipedia, <a href="http://en.wikipedia.org/wiki/Stirling%27s_approximation">Stirling's approximation</a>.
%F A229495 Equals exp(1)/sqrt(2*Pi).
%F A229495 Equals lim_{n->oo} (A001142(n)^(1/n)*sqrt(n)/(exp(n/2))) (Furdui, 2013). - _Amiram Eldar_, Mar 26 2022
%F A229495 Equals Product_{n>=1} (1 + 1/n)^(n+1/2)/e. - _Amiram Eldar_, Jul 08 2023
%F A229495 Equals exp(A110544). - _Amiram Eldar_, May 30 2025
%e A229495 1.0844375514192275466115773134229479858...
%p A229495 evalf(exp(1)/sqrt(2*Pi),120); # _Muniru A Asiru_, Oct 07 2018
%t A229495 RealDigits[E/Sqrt[2Pi],10,120][[1]] (* _Harvey P. Dale_, Jan 21 2017 *)
%o A229495 (PARI) exp(1)/sqrt(2*Pi) \\ _Ralf Stephan_, Sep 26 2013
%o A229495 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(1)/Sqrt(2*Pi(R)); // _G. C. Greubel_, Oct 06 2018
%Y A229495 Cf. A001113 (e), A019727 (sqrt(2*Pi)), A001142, A110544.
%K A229495 nonn,cons
%O A229495 1,3
%A A229495 _John W. Nicholson_, Sep 24 2013
%E A229495 More terms from _Ralf Stephan_, Sep 26 2013
%E A229495 Corrected and extended by _Harvey P. Dale_, Jan 21 2017