cp's OEIS Frontend

A248859 Decimal expansion of log(sqrt(2*Pi))/e, a constant appearing in the asymptotic expansion of (n!)^(1/n).

%I A248859 #28 Apr 12 2022 04:24:13
%S A248859 3,3,8,0,5,8,5,9,4,0,6,6,2,3,9,9,0,2,3,7,0,2,7,9,4,5,0,9,6,1,5,1,8,8,
%T A248859 7,4,2,6,8,5,1,3,7,5,8,3,4,0,2,0,7,8,2,5,1,6,8,6,1,8,1,2,4,9,6,9,8,6,
%U A248859 5,8,9,3,0,4,6,0,2,4,6,3,4,0,3,9,9,2,7,5,5,2,7,6,6,3,9,2,0,5,8,6,5,8,1,6,2
%N A248859 Decimal expansion of log(sqrt(2*Pi))/e, a constant appearing in the asymptotic expansion of (n!)^(1/n).
%H A248859 G. C. Greubel, <a href="/A248859/b248859.txt">Table of n, a(n) for n = 0..10000</a>
%H A248859 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2021, p. 57.
%H A248859 Shafiqur Rahman and Leonard Giugiuc, <a href="https://cms.math.ca/publications/crux/issue?volume=43&amp;issue=9">Problem 4285</a>, Crux Mathematicorum, Vol. 43, No. 9 (2017), pp. 399 and 401; <a href="https://cms.math.ca/publications/crux/issue?volume=44&amp;issue=9">Solution to Problem 4285</a>, ibid., Vol. 44, No. 9 (2018), p. 395.
%F A248859 Equals lim_{n -> infinity} (n!)^(1/n) - n/e - log(n)/(2*e).
%F A248859 Equals A075700/A001113 = A061444/A019762. - _Amiram Eldar_, Apr 12 2022
%e A248859 0.3380585940662399023702794509615188742685137583402...
%t A248859 RealDigits[Log[Sqrt[2*Pi]]/E, 10, 105] // First
%o A248859 (PARI) log(2*Pi)/2/exp(1) \\ _Charles R Greathouse IV_, Apr 20 2016
%o A248859 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Log(2*Pi(R))/(2*Exp(1)); // _G. C. Greubel_, Oct 07 2018
%Y A248859 Cf. A001113, A019762, A061444, A075700 (log(sqrt(2*Pi))).
%K A248859 nonn,cons,easy
%O A248859 0,1
%A A248859 _Jean-François Alcover_, Mar 03 2015