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

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, 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, 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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2021, p. 57.

Shafiqur Rahman and Leonard Giugiuc, Problem 4285, Crux Mathematicorum, Vol. 43, No. 9 (2017), pp. 399 and 401; Solution to Problem 4285, ibid., Vol. 44, No. 9 (2018), p. 395.

Formula

Equals lim_{n -> infinity} (n!)^(1/n) - n/e - log(n)/(2*e).

Equals A075700/A001113 = A061444/A019762. - Amiram Eldar, Apr 12 2022

Example

0.3380585940662399023702794509615188742685137583402...

Mathematica

RealDigits[Log[Sqrt[2*Pi]]/E, 10, 105] // First

Prog

(PARI) log(2*Pi)/2/exp(1) \\ Charles R Greathouse IV, Apr 20 2016
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Log(2*Pi(R))/(2*Exp(1)); // G. C. Greubel, Oct 07 2018

Crossrefs

Cf. A001113, A019762, A061444, A075700 (log(sqrt(2*Pi))).

Sequence in context: A232459 A175566 A349425 * A171543 A079073 A165507

Adjacent sequences: A248856 A248857 A248858 * A248860 A248861 A248862

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Mar 03 2015

Status

approved