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%I #19 Feb 27 2021 13:20:38
%S 0,1,9,0,0,3,1,1,4,8,9,8,1,4,0,4,4,7,6,2,0,2,9,2,0,9,4,3,2,9,7,3,4,2,
%T 7,0,0,9,4,4,6,2,7,0,1,5,0,0,3,4,1,3,7,6,0,4,2,2,4,2,5,1,8,7,4,8,0,4,
%U 2,5,7,8,9,3,1,5,4,3,2,6,4,0,5,9,3,2,3,1,8,2,4,5,1,5,4,6,3,2,4,1,8,2,6,2,4
%N Decimal expansion of the constant 6*exp(psi(1/6) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.
%C This constant appears in _Benoit Cloitre_'s generalized Euler-Gauss formula for the Gamma function (see Cloitre link) and is involved in the exact determination of asymptotic limits of certain order-6 linear recursions with varying coefficients (see A097681 for example).
%D A. M. Odlyzko, Linear recurrences with varying coefficients, in Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grotschel and L. Lovasz, eds., Elsevier, Amsterdam, 1995, pp. 1135-1138.
%H G. C. Greubel, <a href="/A097671/b097671.txt">Table of n, a(n) for n = 0..2500</a>
%H Benoit Cloitre, <a href="/A097679/a097679.pdf">On a generalization of Euler-Gauss formula for the Gamma function</a>, preprint 2004.
%H Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html">Introduction to the Gamma Function</a>.
%H Andrew Odlyzko, <a href="http://www.dtc.umn.edu/~odlyzko/doc/asymptotic.enum.pdf">Asymptotic enumeration methods</a>, in Handbook of Combinatorics, vol. 2, 1995, pp. 1063-1229.
%F c = 1/sqrt(12)*exp(-Pi/2*sqrt(3)).
%e c = 0.01900311489814044762029209432973427009446270150034137604224...
%t RealDigits[1/Sqrt[12]*E^(-Pi/2Sqrt[3]), 10, 104][[1]] (* _Robert G. Wilson v_, Aug 27 2004 *)
%o (PARI) 6*exp(psi(1/6)+Euler)
%Y Cf. A097663-A097670, A097672-A097676.
%K cons,nonn
%O 0,3
%A _Paul D. Hanna_, Aug 25 2004
%E More terms from _Robert G. Wilson v_, Aug 27 2004
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